Multilayer parameter-varying fusion and deposition strategies for additive manufacturing

ABSTRACT

The invention encompasses compositions and methods for designing or producing three-dimensional articles layer-by-layer, whereby the specific approach to build-up a region of a single layer by fusion, deposition of material, or other path-based process or non-path process that creates track-like geometries requires either differing track or track-like geometry, or track or track-like geometry printing parameters, within a region of a single layer or within adjoining regions of multiple layers, is disclosed. Employing this method, single layer or multilayer parameter-varying fusing and deposition strategies can be generated that reduce article fabrication time and improve article physical properties, in part by targeting a distribution of scan paths that satisfy covering problem overlap and/or dense packing criteria. Additionally, methods and compositions for designing or producing three-dimensional articles by altering the thickness of a material layer deposited during a print relative to the slice thickness or net displacement of a stage or of a material and/or energy-depositing print head, are disclosed. Employing this method can result in the reduction of article fabrication time and/or the improvement of printed article physical properties, where these results advantageous to printing are dependent on the print process, material properties, and feedstock properties employed during the print.

FIELD OF THE INVENTION

The invention encompasses compositions and methods for designing orproducing three-dimensional articles layer-by-layer, whereby thespecific approach to build-up a region of a single layer by fusion,deposition of material, or other path-based process or non-path processthat creates track-like geometries requires either differing track ortrack-like geometry, or track or track-like geometry printingparameters, within a region of a single layer or within adjoiningregions of multiple layers, is disclosed. Employing this method, singlelayer or multilayer parameter-varying fusing and deposition strategiescan be generated that reduce article fabrication time and/or improvearticle physical properties, in part by targeting a distribution of scanpaths that satisfy covering problem overlap and/or dense packingcriteria. Additionally, methods and compositions for designing orproducing three-dimensional articles by altering the thickness of amaterial layer deposited during a print relative to the slice thicknessor net displacement of a stage or of a material and/or energy-depositingprint head, are disclosed. Employing this method can result in thereduction of article fabrication time and/or the improvement of printedarticle physical properties, where these results advantageous toprinting are dependent on the print process, material properties, andfeedstock properties employed during the print.

BACKGROUND

Additive manufacturing (AM), often called 3D printing, can be describedas a process of building up a three-dimensional solid or porous articlecomprised of one or more materials by fusing, bonding, or otherwiseattaching successive layers of the article to one another. The layers inAM are often represented conceptually or in a computer or drawing by aset of finite-thickness slices of a three-dimensional article, whereeach slice is most commonly the intersection between the article and oneof a set of stacked finite-thickness Euclidean planes, where the planesare defined as those with normal vector in the chosen direction ofbuild-up of the article. Slices can be defined by a different set ofsections other than planes, but the sections generally maintain theproperty that when all sections of the article from the set are combinedin specified order, the three-dimensional article is retrieved. By wayof example, a non-planar set of slices might be the intersection betweenthe article and a number of radially increasing hemi-spherical surfaces(the sections) where the increase in radius of curvature between eachsuccessive section is the radial thickness of the preceding section. Inthis case, the build-up direction at every point on the slice might bein the direction from the spherical-center of the section to the point(radially outward).

There are multiple AM article fabrication methods, including fuseddeposition modeling, stereolithography, selective laser sintering,binder jetting, material jetting, multi-jet fusion, powder bed fusion,directed energy deposition, laminated object manufacturing, and manyothers. In each of these methods, a certain type of printer is employed,where the printer is the machine or system of machines that constructslayers and successively fuses, bonds, or otherwise attaches these layersto one another in order to create a three-dimensional article.Generally, the printer and its components are controlled by a computer,where this computer has stored in its memory certain data representinginstructions for the printer's hardware components on how toapproximately produce each slice of a three-dimensional article andfuse, bond, or otherwise attach the layer represented by each slice toprevious and successive layers. Those instructions are also generated bya computer (the same or different), where the latter computer contains adata-based geometric representation of a three-dimensional article, thecapability (through software) to divide these geometric representationsinto slices, and the capability (through software) to issue the datarepresenting the instructions, readable by one or more printers, toapproximately produce and fuse, bond, or otherwise attach successivelayers to one another.

Printers collectively are capable of fabricating objects from a widevariety of different materials, including by way of example polymers,thermoplastics, metals, ceramics, glasses, and composite combinations ofany of these. Each type of printer is, however, generally targetedtoward producing three-dimensional objects from a more narrow range ofmaterials. For example, stereolithography printers generally printobjects from photopolymers by first depositing a thin layer ofphotopolymer on a surface, and then exposing a region of that surfacerepresentative of a slice of the article at that layer to UV or otherlight in order to harden or solidify that region. The layering andexposure process is then repeated at least once, but generally amultitude of times, where each layer deposited builds the height of thearticle at every point in the build-up direction, and where eachsuccessive region exposed is in the approximate shape of a successiveslice of the same three-dimensional article. Generally, the successivelayers that comprise the article fabricated sit atop a build platform,shown in FIG. 1, that in turn sits atop a precision stage, and thisprecision stage is lowered a certain distance after each deposition stepand exposure step, where this distance is roughly equal to the thicknessof the layer of photopolymer deposited in each step.

Generally in printing, the approximate average thickness of each layeris roughly equivalent to the absolute value of the distance traversed byeither; a) a stage, as in the case of stereolithography printing, or b)in some cases where a material or energy-depositing nozzle is used,between a given point on one slice or its representative layer n and thepoint on the successive slice or layer n+1 that is defined as theintersection between 1) a vector starting at the point on n and orientedin the build-up direction, and 2) the successive layer n+1. Thisapproximate thickness for the entirety of each slice or layer, or ateach point on a slice or layer, is generally called the layer thickness;in FIG. 1, by way of example for printing employing a stage, the layerthickness is shown as LT.

In material jetting processes, to fabricate a planar layer, a dispensergenerally deposits a material, often in a suspension, slurry, liquid,gel, powder, or other form, in coordinated adjacent paths, often lines,such that the rough shape of the area covered by a multitude of thesetracks of material is representative of a slice of the article. Materialjetting printers might also deposit energy in addition to material, andthey might deposit one track at a time or many, for example, byemploying more than one nozzle, where different materials could be usedin different nozzles.

Generally, the specific approach used to deposit many adjacent tracks ofmaterial (and/or energy) so as to form the rough shape defined by aslice of the article can be called the scan strategy for that slice orlayer. The order of track production within a layer is not necessarilycritical to the process, though a faster process usually results fromfabricating nearest-neighbor tracks sequentially due to this approachtending to minimize the time expended for each layer in moving the printhead or otherwise redirecting material or energy to produce tracks. Thematerial deposited generally thickens or solidifies a short time afterdeposition of material or energy in the rough shape of its slice. Thetracks deposited have a height that is very roughly equal to that of thelayer thickness and are spaced in a fashion that is generally roughlyconsistent with their width, as shown in FIG. 2, where the spacingbetween adjacent track paths is often call the hatch spacing. As with astereolithography process, a precision stage can used, but in contrastto stereolithography, a nozzle or nozzles, in order to deposit materialfor a successive layer, might also be raised in the build up directionby a distance approximately equal to the layer thickness at that point.

Binder jetting processes are in some ways similar to material jettingprocesses in that for each layer, adjacent tracks of material aredeposited in the rough shape of a slice of a three-dimensional objectrepresentative of that layer, according to any of a number of scanstrategies. However, in a binder jetting process, a thin layer ofpowdered material is first deposited across the entirety of a buildarea, and the material deposited in adjacent paths is a binding agent,or glue, that is cured or otherwise solidified in order to hold thepowder particles in rigid relation to one another. The green articlethat is fabricated in successive layers is comprised of both powderparticles and hardened binding agent.

Powder bed fusion and laser or other sintering processes are similar tobinder jetting processes in terms of powder deposition, but in theseprocesses, an energy source melts or sinters powder particles so that asolid layer is formed either from material that resolidifies aftermelting, or from partially melted (sintered) particles that are roughlyfixed in space in rigid relation to one another. FIG. 3a illustrates twolayers of a scan strategy that is commonly used in powder bed fusion andlaser sintering processes, as well as other printing processes. In thiscase, as is often the case in the other processes just described, thedirection of scan paths, where a scan path is defined as theone-dimensional path along which material is deposited or an energysource scans in order to form a track, can be rotated in a controlledfashion from layer to layer in order to produce desirable physicalcharacteristics in fabricated articles, including by way of exampleincreased isotropy of elastic properties, reduced porosity, or increasedthroughput/reduced costs of printing. FIG. 3b is a top-down image ofscan tracks in a single layer of a powder bed fusion process printedaccording to the scan paths illustrated in FIG. 3a . FIG. 3c is an imageof a section of an article fabricated employing the scan strategydepicted in FIG. 3a . Additionally, some powder bed fusion processesexist that are not path based, but instead pattern based in a similarfashion to stereolithography. In these processes, a pattern of energy isprojected onto a broad area of the build surface as opposed to a smallenergy spot being rastered or scanned over the area.

Some past patents and research have discussed scan strategies that areclaimed to be advantageous to printing in terms of improving articlephysical characteristics or improving economic and/or manufacturingconsiderations of printing. For example, U.S. Pat. No. 5,155,324 datedOctober 13, 1992, discusses a selective laser sintering process in whichover successive layers, scan lines that are parallel and anti-parallelwithin one layer are rotated a given amount in each successive layer.U.S. Pat. No. 7,569,174 dated August 4, 2009, discusses a selectivelaser sintering process whereby each layer in an article is scanned by alaser once with higher energy, covering the entirety of the planarcross-section of the article at that slice, and then scanned at leastone more time at relatively lower energy. The intent of this process isto anneal or further melt each layer of the article, and strengthimprovements up to 100% are reported.

Additionally, there are a number of patents that discuss compositionsfabricated using specific scan patterns. Compositions are often linkedto scan patterns due to the nature of building up a part layer-by-layer,and/or track by track. For example, when articles are fabricated withtracks that are produced by scanning in only one direction (and/oranti-parallel to that direction), article strength, ductility,electrical conductivity, thermal conductivity, and other characteristicsare typically increased in that direction, but decreased in otherdirections, particularly in directions near the two directionsperpendicular to the scanning direction, though this is not a hard andfast rule. This change in article elastic, mechanical, and otherphysical properties is due to the local phase, bonding, and crystallinestructure imparted by the elongated nature of scan tracks and thelamellar nature of layer-wise manufacturing. Grain boundaries and othertypes of chemical/microstructural boundaries tend to form at the edgesof scan tracks, leading to substantial changes in elastic and transportphenomena as a function of the position and concentration of theseboundaries. In the prior example of scanning all tracks in a singledirection, no track boundaries are crossed by progressing in the scandirection (or anti-parallel to it), leading to substantial anisotropy inphysical properties.

There are also a small number of patents and research papers thatdiscuss a specific scan strategy for which not only the angle, but alsothe relative position of scan lines in successive planar layers isspecified. In this method, scan lines are “interleaved” between layerssuch that the scan lines in layer n+1 are placed at the midpoint betweenthe scan lines in layer n, without rotation, as shown in FIG. 4. U.S.Pat. No. 6,596,224 discusses this method for a material jetting or fuseddeposition modeling process, stating that the surface finish of thearticle can be improved by employing such a method over about ˜10 layersnear the physical top of the article. U.S. Pat. No. 6,677,554 discussesthis method for a selective laser sintering process, stating that thenumber of total scan lines and therefore the sum of the lengths of allscan lines can be reduced with this method, leading to an increase inarticle fabrication throughput, and possibly to an increase in articlestrength. The journal article: X. Su and Y. Yang, Research on trackoverlapping during Selective Laser Melting of powders, Journal ofMaterials Processing Technology 212, pp. 2074-2079 (2012), studies thismethod for a selective laser melting (powder bed fusion) process, forthe stated purpose of avoiding nonuniform distribution of energy input.

Definitions:

Packing problem: A packing is a configuration (spatial arrangement) ofnonoverlapping objects in a subregion of d-dimensional Euclidean spaceor d-dimensional curved spaces. A periodic packing in Euclidean space isone in which y objects, called the basis, are contained within a unitcell of volume v_(U) that is periodically replicated in space. The shapeand symmetry of unit cell is defined by “d” lattice basis vectors b (notto be confused with the basis objects). The objects can be of arbitraryshape, including convex (e.g., circles, ellipses, spheres, ellipsoids,cylinders) and concave (e.g., star of David, crosses, stellatedpolyhedra and hyperbolic paraboloids) shapes. Polydisperse packings arethose in which the objects have different sizes and/or shapes. Binarypackings are those that have two different sizes and/or shapes. Ternarypackings are those that have three different sizes and/or shapes. Eachobject is configurationally defined by its coordinate r, which accountsfor both its position and orientation; by way of example, in threedimensions, this coordinate r might include three spatial coordinates(x,y,z) representing object center of mass, and two angular coordinates(θ,φ) representing longitudinal and latitudinal displacements about theobject center. A basic property of a packing is the packing fraction,which is the fraction of space occupied by the objects. The packingfraction of a periodic packing is the total volume of the γ basisobjects within the unit cell divided by v_(U). An efficient packing hasa high packing fraction. The best packing has the highest packingfraction among all packings.

Covering problem: A covering is a configuration of overlapping objectsthat completely covers a subregion of d-dimensional Euclidean space ord-dimensonal curved spaces. A periodic covering in Euclidean space isone in which γ objects, called the basis, are contained within a unitcell of volume v_(U) that is periodically replicated in space. The shapeand symmetry of unit cell is defined by d lattice basis vectors b (notto be confused with the basis objects). The objects can be of arbitraryshape, including convex (e.g., circles, ellipses, spheres, ellipsoids,cylinders) and concave (e.g., star of David, crosses, stellatedpolyhedra and hyperbolic paraboloids) shapes. Polydisperse coverings arethose in which the objects have different sizes and/or shapes. Binarycoverings are those that have two different sizes and/or shapes. Ternarycoverings are those that have three different sizes and/or shapes. Eachobject is configurationally defined by its coordinate r, which accountsfor both its position and orientation; by way of example, in threedimensions, this coordinate r might include three spatial coordinates(x,y,z) representing object center of mass, and two angular coordinates(θ,φ) representing longitudinal and latitudinal displacements about theobject center. A basic property of a covering is the covering density,which is the total volume of the objects per unit volume. The coveringdensity of a periodic covering is the total volume of the y basisobjects within the unit cell divided by v_(U). An efficient covering hasa low covering density. The best covering has the lowest coveringdensity among all coverings.

Track cross section: The average of the shapes defined by theintersection of a surface, most simply a plane, and a single track ofmaterial, where the intersection is taken at various points along thescan path of the track, we define as a track cross section. Most simply,a track cross section is formed by the intersection of a track and aplane with unit normal parallel to the direction of track or scanpropagation at that point, and where an average shape is taken byspatial averaging over a plurality of these intersections at differentpoints along the track or scan path. For the sake of clarity, we willrefer to track cross sections formed in this fashion as path-tangenttrack cross sections, recognizing however that the choice of thetrack-intersecting surface and its orientation are not essential toforming a track cross section, though a consistent choice ofintersecting-surface and orientation is useful in identifyingdifferences between tracks and in designing scan strategies. FIG. 5includes images of several different path-tangent track cross sectionsfrom a laser powder bed fusion printer, where the difference in shapeand size of the track cross sections is dependent on the printingparameters including but not limited to laser power and scan speed.

One or more track cross sections, with or without fixed angularorientation, can be used as a basis set for a covering problem solution.The same holds true for geometric approximations (the simplest being acylinder) of one or more actual tracks in three-dimensions.Additionally, more simply, a packing consisting of one or moresame-sized or differently-sized objects, most simply (but not limited tobeing) disks in two-dimensions and cylinders in three-dimensions,serving as a basis, respectively, in a two-dimensional orthree-dimensional unit cell, can be thought of as representative oftrack cross sections in two dimensions or approximations of tracks inthree dimensions, and therefore employed to generate scan strategies. Inthis way, a mapping exists being track cross sections, packings and scanstrategies, and track cross sections, covering problem solutions andscan strategies.

Slice Thickness, Layer Thickness, Material Thickness, and NetDisplacement: Generally, slice thickness, material layer thickness(powder layer thickness before energy or material deposition in printingprocesses involving powder beds), and the absolute value of netdisplacement of a stage or material- (and possibly energy-) depositingprint head at each point, or for each slice or its representative layer,are all thought of as the same concept, called the layer thickness.Fundamentally though, slice thickness, material/powder thickness, andnet displacement need not be the same; in particular, employingdifferent values for the material thickness and net displacement in aprint can yield positive benefits to printed part quality and theprinting process, as we describe in detail later in this document.

The term slice thickness is used herein to refer to the thickness of aslice of a three-dimensional article in the vicinity of a given point onthat slice, with “slice” as defined previously. We employ the term slicein reference to the design, whereas we generally employ the term layerin reference to the fabricated article. In this usage, the thickness ofthe material layer and the thickness of the slice are not necessarilythe same, either in average or at a particular point.

The average material layer thickness of a single layer or the thicknesslocal to a specific point in a layer can vary substantially, and it canvary significantly from the maximum height of the track. In FIG. 2,track height varies locally, with variations in height occurringperiodically on the order of track width; this is also the case in asimilar fashion for powder bed fusion printing, as may be seen in FIGS.3b, 3c , and 5, and generally for all scan and track based, or similar,printing processes. Consequently, at a local level, the thickness of thelayer or track of material deposited is not the same as the thickness ofthe slice: only the average deposited material thickness over manytracks and many layers is approximately the slice thickness. This latterstatement is made under the assumption that the length scale representedin the design is approximately replicated by the printer in fabricatingthe physical article.

In powder bed fusion printing and other powder-based printing processes,the differences in the concepts of slice and layer thickness are alsodue both to the local variation in the thickness of the layer of powderdeposited, which varies laterally on the order of a few powder particlediameters according to particle size and shape distribution, and inpowder bed fusion to the fact that track depths tend to be much largerthan slice thicknesses due to the practice of remelting previouslymelted layers in order to achieve near-full density fabricated articles.Further, as is described in this invention, the material thickness orpowder thickness, defined simply as the average thickness of depositedmaterial in the vicinity of a point (before binding, fusing, melting,sintering, or other print process is applied), does not need to be thesame as the slice thickness or the average layer thickness. This is animportant consideration from the perspective of track shape andtherefore track cross section shape because varying the materialthickness can alter track and track cross section shape.

Often, the material thickness is intended to be roughly constant acrossa layer of deposited material. Nevertheless, the thickness of adeposited layer is dependent on material characteristics and printerparameters, for example, in the cases where a powder shuttle is used todeposit or spread powder, the distance between the blade, wiper, roller,or other spreading tool on the shuttle and the built-up physical articleheight has a strong influence on powder thickness. This latter distanceis often controlled by a stage, which during the process of printing alayer may move several times in or against the build-up direction of thearticle. Over the course of printing a layer, the net movement of thisstage is one example of the net displacement. For a print processinvolving a powder bed and a stage, the net displacement at a givenpoint is most similar to the slice thickness at that point. Critically,because powder may be deposited at any displacement of the stage, thepowder thickness and the net displacement can be individuallycontrolled, meaning that the net displacement (slice thickness) andpowder thickness do not need to be the same. FIG. 6 is an example ofthis concept where slice thickness and net displacement are constantover the slice shown, and where a 35 um powder thickness is employed for50 um net displacement (and 50 um slice thickness).

The material (or powder) thickness and slice thickness may also vary foran AM process with a print head and no stage, or with both a stage and aprint head; the average thickness of material deposited in the vicinityof a point on a slice does not need to be the same as the netdisplacement of the print head at that same point. By way of example, aslice thickness that is constant across the slice from position x=0 tox=L could be employed for layer n, with average deposited materialthickness varying linearly across that distance, with smallest materialthickness to microns of material deposited on at x=0 and largestmaterial thickness t_(L) microns of material deposited at x=L.

Filling Strategies, Contours Scans, Support Structures, Print Lattices,and Others: Printers and printing that employ path, scan, and trackbased processes have the capability to employ different printingparameters to distinctly structurally different regions of an article,as defined on the scale of the article. Critically, while differentprint parameters can be employed within a single layer in order toimplement the families of scan strategies that include; fillingstrategies, contour scans, support structures, print lattices, andothers; different print parameters are not employed within the samestrategy, and different strategies are employed across regions of thearticle defined by (larger) targeted article geometry rather than in aperiodic, alternating, or other fashion defined on the (smaller) scaleof scan tracks.

Contour scans are often employed on the surfaces of parts in order to:improve part surface finish, improve the geometric match between thefabricated article and the plan, image, or computerized data intended tobe fabricated, or to reduce porosity around article surfaces, amongother reasons. Multiple contour scan tracks can be placed side-by-side,but the number of such side-by-side tracks is often limited to one, two,or three.

Support structures are employed in order to prevent fabricated articlewarping, to conduct heat away from thermally isolated regions of theprint, and to hold the article to the build platform, among otherreasons. Support structures are often produced using evenly spacedsingle scans, with unprinted space between the scans, that produce aseries of interlinked thin walls, spikes or columns. Distinctively,support structures are not meant to be part of a finished article andare nearly always cut away, dissolved away, or otherwise removed afterprinting.

Print lattices, not to be confused with the mathematical concept oflattice defined previously, are scaffolding-like structures that arecomposed of single three-dimensional units or voxels of space containingboth printed and unprinted material, replicated many times over to covera region of space spanning many voxels. Print lattices can be describedas strut and node structures, in that they consist of nodes from whichstruts of printed material extend in various directions, connecting withother struts at other nodes. They can be generated with single scanslike support structures, or each strut can be produced by multipleadjacent overlapping or nearly overlapping tracks.

Filling strategies are designed to fill space, and are distinct from theprevious strategies in that they are intended to produce a solid regioneither with very low porosity, or with a stochastic porosity where poresizes are roughly on the order of hatch spacing or smaller. Someexamples of fill strategies are depicted in FIGS. 3a and 4. Fillstrategies can also be employed to fill the struts and nodes of printlattices where those struts are not formed by single tracks.Additionally, the delineation between fill strategies and contour scansis somewhat blurred when larger numbers of contour scans are employednear the surfaces of printed articles. Further, some filling strategiesand other strategies are termed skins, or other terms, implying that thelateral extent of such filling strategies is significantly greater thantheir thickness.

SUMMARY OF THE INVENTION

The present invention relates to additive manufacturing scan strategies,and related methods, systems, and compositions, and methods and systemsfor altering the thickness of a material layer deposited during a printrelative to the net displacement of a stage or of a material and/orenergy-depositing print head, and/or relative to the article slicethickness. The applications where this present invention is valuableinclude but are not limited to: 1) fused deposition modeling, 2)material jetting, 3) binder jetting, 4) powder bed fusion, 5) selectivelaser sintering, 6) multi-jet fusion, 7) directed energy deposition, 8)direct metal deposition, 9) Electron beam additive manufacturing, 10)arc plasma sintering additive manufacturing, and other additivemanufacturing methods where generally defined scan paths and tracks areemployed, and in additive manufacturing methods where material or energydeposition patterns over a more broad area generate periodic surfaceheight variations similar to those exhibited by a series of tracks.Hereafter, discussions of tracks, track cross sections, scan strategies,and scan paths include both the additive manufacturing methods, systems,and compositions where scan paths and tracks are employed, and the caseswhere material or energy deposition patterns over a broader areagenerate surface variations similar to those exhibited by a series oftracks.

In one embodiment, the present invention contemplates an additivelymanufactured composition in which track geometry or track cross sectiongeometry is substantially similar for all or nearly all of the scantracks in a region of a printed layer, but different for all or nearlyall of the tracks in an adjoining region of a prior or successive layer.In one embodiment, the present invention contemplates an additivelymanufactured composition in which more than one shape or size of trackor track cross section is employed in manufacturing a layer, layers, orportions thereof, and where the configurations of the tracks or trackcross sections are targeted to differ in coordinated fashion within eachlayer, layers, or portions thereof. In one embodiment, the presentinvention contemplates an additively manufactured composition in whichthe configurations of tracks or track cross sections consisting of aplurality of different shapes or sizes in a region of an article arespecified with positions according to crystallographic point patterns,where those tracks cover a unit cell of such a pattern in a fashion suchthat unprinted area in the cell is not present in sizes larger than thelargest track (or its cross section), and where parts of at least twoadjacent cells are present in the part of each layer contained withinthe region.

In one embodiment, the present invention contemplates an additivelymanufactured composition in which a plurality of different sized and/orshaped tracks or track cross sections are used in a solution to a two(for track cross section) or three (for tracks) dimensional coveringproblem, and where the configurations of the tracks or track crosssections in the solution are used to define the relative position ofscan paths across a region including parts of or all of one or moresuccessive layers in a multi-layer scan strategy.

In one embodiment, the scan tracks discussed in paragraphs two and threeof this “Summary of the Invention” section in a region encompassingparts of two or more successive layers are all or nearly all parallel oranti-parallel. In one embodiment, the scan tracks discussed inparagraphs two and three of this section are in a region of a givenlayer all or nearly all rotated by a specific angle relative to those inan adjoining region of the previous layer. In one embodiment, the scantracks discussed in paragraphs two and three of this section are in aregion of a given layer all or nearly all parallel or anti-parallelrelative to those tracks in an adjoining region of the prior layer, butthe tracks in an adjoining region of the successive layer are rotated bya specified angle. In one embodiment, the scan tracks discussed inparagraphs two and three of this section are ordered chronologically,for each layer that is partially or entirely contained within a regionof an article, such that either adjacent tracks or non-adjacent tracksare printed successively.

In one embodiment, the present invention contemplates a method ofdesigning scan strategies where track geometry or track cross sectiongeometry is targeted to be substantially similar for all or nearly allof the scan tracks in a region of a printed layer, but different for allor nearly all of the tracks in an adjoining region of a prior orsuccessive layer. In one embodiment, the present invention contemplatesa method of designing scan strategies using more than one shape or sizeof track or track cross section where the configurations of the tracksor track cross sections are targeted to differ in coordinated fashionfor scan tracks in a region of a printed layer. In one embodiment, thepresent invention contemplates a method of designing scan strategieswhere the configurations of tracks or track cross sections consisting ofa plurality of different shapes or sizes in a region of an article arespecified with positions according to crystallographic point patterns,where those tracks cover a unit cell of such a pattern in a fashion suchthat unprinted area in the cell is not present in sizes larger than thelargest track (or its cross section), and where parts of at least twoadjacent cells are present in the part of each layer contained withinthe region.

In one embodiment, the present invention contemplates a method ofdesigning scan strategies where a plurality of different sized and/orshaped tracks or track cross sections are used in a solution to a two(for track cross section) or three (for tracks) dimensional coveringproblem, and where the configurations of the tracks or track crosssections in the solution are used to define the relative position ofscan paths across a region including parts of or all of one or moresuccessive layers in a multi-layer scan strategy.

In one embodiment, the scan tracks discussed in paragraphs five and sixof this “Summary of the Invention” section in a region encompassingparts of two or more successive layers are all or nearly all parallel oranti-parallel. In one embodiment, the scan tracks discussed inparagraphs five and six of this section are in a region of a given layerall or nearly all rotated by a specific angle relative to those in anadjoining region of the previous layer. In one embodiment, the scantracks discussed in paragraphs five and six of this section are in aregion of a given layer all or nearly all parallel or anti-parallelrelative to those tracks in an adjoining region of the prior layer, butthe tracks in an adjoining region of the successive layer are rotated bya specified angle. In one embodiment, the scan tracks discussed inparagraphs five and six of this section are ordered, for each layer thatis partially or entirely contained within a region of an article, suchthat either adjacent tracks or non-adjacent tracks are printedsuccessively.

In one embodiment, the present invention contemplates a method ofadditive manufacturing where the slice thicknesses or net displacementsfor each layer within a region of an article are varied in order toalter the average geometric shape and/or area of tracks (and/or trackcross sections) within the region. In one embodiment, the materialthickness of a layer or layers within a region of an article isdifferent (either greater or lesser) from the slice thickness or netdisplacement, and where the slice thickness or net displacement for theparts of each layer encompassed within the region may be either the sameor different from that of other layers within the region. In oneembodiment, the thickness of material deposited for a layer or layerswithin a region of an article for the embodiments discussed in thisparagraph thus far are different (either or greater or lesser) from theslice thickness or net displacement for the parts of the layer or layersin that region in such a fashion as to alter the average geometric shapeand/or size of scan tracks within the parts of the layer or layersencompassed by the region.

BRIEF DESCRIPTION OF THE FIGURES:

FIG. 1a is a schematic view of a conventional stereolithographyapparatus, demonstrating the standard layering and exposure process. Byway of example, a build platform is mounted upon a precision stageplaced within a bath of photocurable polymer. The build platform ispositioned such that a thin layer of uncured polymer, comparable to thelayer thickness (LT) to be built-up, is deposited on a surface andsubsequently exposed to an energy source in an area representative of aslice of the article to selectively harden or solidifying the material.

FIG. 1b is a schematic drawing of a build platform in astereolithography apparatus, as described in FIG. 1 a, being lowered asimilar distance (LT) to produce a new layer of uncured polymer. Thisexposure and layering process, shown here and within FIG. 1 a, isrepeated, where each successive region exposed and layer depositedbuilds the height of the article at every point in build-up direction inthe approximate shape of a successive slice of the samethree-dimensional article.

FIG. 2 is an illustration of planar layer build-up of an article throughmaterial jetting. One, or more, nozzle(s) deposits material(s) alongcoordinated adjacent paths spaced by a periodic distance called thehatch spacing h. The deposited material creates tracks of widthsconsistent with the hatch spacing and heights approximately equal to thelayer thickness (LT) of the sliced article such that the rough shape ofthe area of the tracks is representative of the slice of the article.Material for successive slices of the same three-dimensional article canbe deposited through a combination of these scan paths along with adistance offset oriented in the build-up direction approximately equalto the layer thickness at that point, achieved through the motion of aprecision stage or of the dispensing nozzles.

FIG. 3a is a schematic drawing illustrating an energy deposition scanstrategy commonly employed in powder bed fusion and laser sinteringprocesses. In this example, the scan strategy is composed of a singlecontour path, representative of the lateral cross section of the sliceof the article, and a multitude of parallel, adjacent paths separated byhatch spacing h, to achieve a contiguous area (or fill) of the slice ofthe article upon powder consolidation. An energy source scans theprescribed paths to melt or sinter powder particles that subsequentlyresolidify to form a solid layer. Scan strategies need not be identicalnor similar between layers—incremental rotation or translation of scanpaths are employed. By way of example, between layer n and layer n+1representing successive slices of the article, the fill paths arerotated in a controlled fashion by a certain angle increment, from angleθ_(n) to θ_(n+1).

FIG. 3b is an optical micrograph of the top of a single layer of steelscan tracks produced by powder bed fusion, employing a scan strategysimilar to that described in FIG. 3a . Reproduced from I. Yadroitsev P.Krakhmalev, and I. Yadroitsava, Hierarchical design principles ofselective laser meting for high quality metallic objects, AdditiveManufacturing 7, pp. 45-56, 2015.

FIG. 3c is an optical micrograph of an etched vertical cross section ofa multilayer article produced by powder bed fusion, employing a scanstrategy similar to that described in FIG. 3a . The cross sections ofthe resolidified powder along the scan tracks show the complex layeredstructure and isotropy imparted through controlled rotation of scanpaths between layers. Reproduced from I. Yadroitsev P. Krakhmalev, andI. Yadroitsava, Hierarchical design principles of selective laser metingfor high quality metallic objects, Additive Manufacturing 7, pp. 45-56,2015.

FIG. 4 is a schematic drawing illustrating a specific implementation ofa scan strategy as described in FIG. 3a . In this method, the positionsof scan paths are defined both within a given layer and relative tosuccessive layers such to achieve an “interleaved” pattern. For example,in layer n, a multitude of parallel, adjacent scan lines are separatedby hatch spacing h, representing the area fill of the slice of thearticle. The fill scan lines in successive planar layers, layer n+1,likewise are separated by hatch spacing h but are translated laterallyrelative to the prior layer by a distance equal to half of the hatchdistance, placing the scan lines of layer n+1 at the midpoint betweenthe scan lines in layer n.

FIG. 5a is an image of the path-tangent track cross section of astainless steel scan line printed by laser power bed fusion with a laserpower of 50 W and laser scanning speed of 60mm/s. Reproduced from I.Yadroitsev, A. Gusarov, I. Yadroitsava, and I. Smurov, Single trackformation in selective laser melting of metal powders, J. Mater.Process. Technol. 210, pp. 1624-1631, 2010.

FIG. 5b is an image of the path-tangent track cross section of astainless steel scan line printed by laser power bed fusion with a laserpower of 50 W and laser scanning speed of 120 mm/s. It is of note thechanges of the shape and size of the cross section, relative to FIG. 5a, due to the increase of scanning speed. Reproduced from I. Yadroitsev,A. Gusarov, I. Yadroitsava, and I. Smurov, Single track formation inselective laser melting of metal powders, J. Mater. Process. Technol.210, pp. 1624-1631, 2010.

FIG. 5c is an image of the path-tangent track cross section of astainless steel scan line printed by laser power bed fusion with a laserpower of 300 W and laser scanning speed of 800 mm/s. The shape of thecross section is elongated compared to FIG. 5a and FIG. 5b . Reproducedfrom C. Kamath, B. El-dasher, G. F. Gallegos, and W. E. King, and A.Sisto, Density of additively-manufactured, 316L SS parts using laserpowder-bed fusion at powers up to 400W, Int. J. of Adv. Manuf. Technol.74, pp. 65-78, 2014.

FIG. 5d is an image of the path-tangent track cross section of astainless steel scan line printed by laser power bed fusion with a laserpower of 300 W and laser scanning speed of 1500 mm/s. As shown incomparison with FIG. 5a -5 c, aspects of the shape and size of the crosssection of resolidified material, including but not limited to thecircularity, contact angle, width, amount of material buildup, anddepth, are dependent on the printing parameters including but notlimited to laser power and scan speed. Reproduced from C. Kamath, B.El-dasher, G. F. Gallegos, and W. E. King, and A. Sisto, Density ofadditively-manufactured, 316L SS parts using laser powder-bed fusion atpowers up to 400 W, Int. J. of Adv. Manuf. Technol. 74, pp. 65-78, 2014.FIG. 6a is a schematic illustration of an example of a powder basedprocess to define the material thickness (MT) used in the AM productionof an article. The build platform is lowered by a precision stage by 35um to form a gap in the powder bed and a roller infills powder from aseparate supply into the gap. This defines the material thickness as 35um.

FIG. 6b is a schematic illustration of motion of the build platform in apowder based AM process immediately following powder deposition, asdescribed in FIG. 6a . Further displacement of the build platform priorto the consolidation of the powder can be used to define a netdisplacement (ND) greater than, equal to, or less than the materialthickness (MT).

FIG. 6c is a schematic illustration of a powder based process in whichthe net displacement (ND) and material (powder) thickness (MT) have beenindependently controlled and can, but need not, differ. The net motionof the precision stage in aggregate between all steps prior toconsolidation of the powder, FIG. 6a and FIG. 6b , defines the total netdisplacement, in this case as 50 um, while the material thickness is 35um as defined by the layering process shown in FIG. 6 a.

FIG. 7a is a unit cell of a dense packing of binary disks, from which amulti-parameter scan strategy can be derived.

FIG. 7b is a covering problem solution for three different sized andshaped objects with fixed angular orientation and in a 2:1:1 ratio withtwo larger objects and one each of the smaller two objects (mirrorimages of one another) per unit cell. In this case the objects'geometries are meant to represent path-tangent track cross sections fortracks generated from two distinct sets of AM track geometry parameters{P^(j) _(i)}₁ and {P^(j) _(i)}₂ in a laser sintering, powder bed fusion,or similar process, though this covering problem solution could beapplied to any additive manufacturing scan or track based process, oradditive manufacturing process generating surface patterns similar tothose produced in a track or scan based process. The labels 1, 2, and 3are intended to represent a chronological ordering for layer production,where such ordering is not intrinsic to the solution but rather has beenimposed. The use of mirror-image smaller objects is meant to reflect thesubtle difference in geometry that might result from printing a track ina position over a surface with asymmetric height variations (in thiscase, on the top, off-centered, of a previously printed scan track).

FIG. 7c is an illustration of a cross-sectional view layer of powder orother material deposited on top of an already-printed layer, layer 1asdescribed in FIG. 7b , with filled-dots in the already-printed layerrepresenting the scan paths scanning in a direction perpendicular to theplane of the illustration.

FIG. 7d is an illustration of a possible result of printing layer 2, as,described in FIG. 7b , with scan paths parallel or anti-parallel tothose in layer 1. The illustration of remaining unconsolidated powder orother material indicates the possible presence of sintered material.Though the path-tangent track cross sections depicted are indicative ofa parallel or anti-parallel scan direction relative to the paths oflayer 1, layer 2 paths could be directed at a specified (or arbitrary)angle from that of the layer one paths, or along contours with changingangle relative to the layer 1 paths as the scan progresses.

FIG. 8 is an image of a path-tangent track cross section of a partprinted with a single track scan strategy consisting of repeating layersof a thermoplastic (polylactic acid) printed by material jetting,employing the basic scan paths as those described for Fig Gb. Togenerate each track, the same settings were used as described for FIG.12, except nozzle scan speed was 1800mm/m and extrusion ratio was 0.35.The settings used to fabricate this part are the default settings forthe Prusa i3, where these settings are optimized to minimize porositysimultaneously with minimizing mechanical failures, surface roughness,and geometric deformities of the part. Measured porosity for this partwas 8%.

FIG. 9 is an image of a cross section of a part printed by materialjetting of a thermoplastic polymer employing the same scan strategy asfor FIG. 8, but with extrusion volume ratio setting of 0.52, equal tothe average extrusion volume ratio setting employed for the part shownin FIG. 10. In this case, excess material was extruded, and the printerfailed to build the part in entirety. This was the result of too muchmaterial being extruded (excess overlap), which also led to extremelypoor surface finish and geometric accuracy, variable porosity across thepart and higher porosity away from part edges. Measured part porosityaway from the edges of the part averaged 7%. It is notable that despitethe much larger average volume extrusion ratio of 0.52 employed for thispart relative to 0.35 of the part shown in FIG. 8, only about 1% morematerial was extruded per unit volume of part printed due to theincreased pressure at the nozzle with higher average extrusion volumeratio settings.

FIG. 10 is an image of a cross section of a part printed by materialjetting of a thermoplastic polymer employing a two track geometry scanstrategy based on the covering problem solution described in FIG. 16.The same settings were used to generate tracks as those described forFIG. 8, except with volume extrusion ratio of 0.69 for the large tracksand 0.34 for the small tracks. Measured porosity for this part was 0.2%.It is clear that a substantial porosity decrease is obtainable with thistwo track approach relative to the approach employed for the part shownin FIG. 8. It is notable that despite the much larger average volumeextrusion ratio of 0.52 employed for this part relative to 0.35 of thepart shown in FIG. 8, only about 8.4% more material was extruded due tothe increased pressure at the nozzle with higher average extrusionvolume ratio settings.

FIG. 11 is an image of a cross section of a part printed by materialjetting of a thermoplastic polymer employing the same basic scan pathsas those for the two track geometry scan strategy described for FIG. 26,and using the same settings to generate the small and large tracks asthose described for FIG. 10. Measured porosity for this part was 2.3%.It is clear that a substantial porosity decrease is obtainable with thistwo track approach relative to the approach employed for the part shownin FIG. 8. It is notable that despite the much larger average volumeextrusion ratio of 0.47 employed for this part relative to 0.35 of thepart shown in FIG. 8, only about 6.4% more material was extruded due tothe increased pressure at the nozzle with higher average extrusionvolume ratio settings.

FIG. 12 is an image of a path-tangent track cross section of a partprinted with a scan strategy consisting of repeating layers of athermoplastic (polylactic acid) printed by material jetting, based onthe covering problem solution detailed in FIG. 16. In this image,printer settings were chosen to demonstrate the difference in scan trackgeometry as opposed to for optimization of part porosity or otherconsiderations. Within a single layer, track cross sections ofalternating track widths are achieved through different scan strategies.The Prusa i3 fused deposition modeling material jetting printer in thiscase employs a nozzle diameter of 400 um, and print parameter settingsinclude a hatch spacing and layer thickness of 200 um, nozzle scan speedof 900mm/min, and 190C extruder temperature, where small width tracksare printed with extruder volume ratio of 0.195 and large width trackswith extruder volume ratio of 0.39. During printing of this part, thesmaller tracks while being printed tended to stick to the most recentlyprinted adjacent larger tracks, thereby leading to the spatialseparation in groups of two tracks, one smaller and one larger, observedin the image.

FIG. 13 is an illustration of replicating unit cells both within andacross layers in order to cover an arbitrary geometric space with acovering problem solution. As is depicted in the figure, tracks can beomitted from individual unit cells in order to better conform to theoverall space intended to be covered.

FIG. 14a is an illustration of how scan tracks conforming to a coveringproblem derived scan strategy employing multiple objects of different AMtrack geometry parameters might be adapted to conform to an objectboundary by removing scan tracks within individual unit cells. The imagedepicted is intended to represent a cross section with normal vectorthat is path-tangent to the scan paths of the covering problem derivedstrategy at the point of cross section; however, such a cross sectionmight not also be path tangent to the border of the article, or to anycontours near that border, at any layer. In general, the tracks derivedfrom the solution to the covering problem are not required to bestraight or parallel to one another or the contours across differentlayers.

FIG. 14b is an illustration of the addition of contour tracks(represented by track cross sections) across several layers at theborder of an article that is designed with a covering problem derivedscan strategy. In this image, the contour track cross sections at theborder are only one layer thick, though they could be multiple layers,or they could consist of an additional covering-problem derived scanstrategy employing multiple AM track geometry parameters. Additionally,the contour track cross sections are depicted as path-tangent crosssections for the sake of simplicity, though the contours might travel isdifferent directions or angles at any cross section of the articlerelative to the tracks of the covering problem derived scan strategy. Itis of note that relative to FIG. 14a , one track of the covering problemderived scan strategy near the object border has been removed, in orderto illustrate a simple process of conforming contours to a coveringproblem derived scan strategy.

FIG. 15 is an illustration describing a choice for the relative positionof scan contours and layering for the same covering problem derived scanstrategy presented in FIG. 7. In this figure, the unit cell described inFIG. 7b has been redefined to include more objects in order to simplifythe approach to layering in a system where a layer is of constant netdisplacement. The new unit cell basis vectors (b₁, b₂) can be written as(3.18, 0.0) and (0.0, 4.0) in units of slice thickness, which isconstant in this case, for a Euclidean coordinate system with the x-axisto the right and the z-axis up. In the same units and coordinates, thewidth (x-axis) of the larger tracks is 1.84, and its total height(z-axis) is 1.79. The width of the smaller tracks is 1.28 and theirheight is 1.31. For this scan strategy, each slice is additionally ofthe same constant net displacement (though material thickness for eachslice is not herein specified). The x-axis spacing between larger scantracks is 1.59, and the x-axis spacings between smaller scan tracks are1.08 and 2.05. It is clear from this image that different unit cells canbe defined for the same covering strategy solution; however, for thisparticular solution, no unit cell with a basis smaller than 4 (2 largetracks cross sections, one each of the mirror-image small track crosssections) can be defined.

FIG. 16 is an illustration of a path-tangent cross section of a coveringproblem solution derived scan strategy with a unit cell including twodifferent objects generated from different AM track geometry parametersemploying a powder bed fusion, laser sintering, or binder jettingprocess. For this particular covering solution, a unit cell of twotracks only is the smallest basis unit cell possible. The basis vectors(b₁,b₂) can be written in units of slice thickness, which is in thiscase constant, as (1.98, 0.00) and (1.00, 1.00), with, in the sameunits, larger track width of 1.46 and height of 1.73, and smaller trackwidth and height of 1.00. In this representation, the x-axis directionis to the right, and the z-axis direction is upwards. Scan spacingbetween tracks is 0.96, amounting a spacing between larger tracks of1.92 and a spacing between smaller tracks of 1.92. Three layers oftracks are shown where these tracks are all parallel at the crosssectioning plane. It is of note, however, that due to the smallvariations in height at the surface of the scan tracks printed in eachlayer, rotation of tracks every layer, every two layers, or every nlayers, might be advisable.

FIG. 17a is a top-down illustration of a scan strategy employing thecovering problem solution unit cell as described in FIG. 16. Layer nconsists of linear scan paths which alternately employ different AMtrack geometry parameters. Adjacent scan tracks need not necessarily beprinted in chronological order.

FIG. 17b is a top-down illustration of a scan strategy employing thecovering problem solution unit cell as described in FIG. 16, in which arotation between successive layers has occurred. Layer n+1 consists ofscan paths and AM track geometry parameters similar to its prior layern, as described in FIG. 17a , that have undergone an in-plane rotationabout the z axis relative to layer n.

FIG. 18a is a top-down illustration of a layer n of a circular scanstrategy implementation of the covering problem solution unit cell asdescribed in FIG. 16. Scan paths of alternating AM track geometryparameter sets are circularly symmetric about the indicated point.

FIG. 18b is a top-down illustration of a successive layer n+1, relativeto layer n described in FIG. 18a , of a circular scan strategyimplementation of the covering problem solution unit cell as describedin FIG. 16.. Successive layer n+1 consists of the superimposed scanpaths of the prior layer n but of the alternate AM track geometryparameter. Scan paths are circularly symmetric about the indicatedpoint, forming the longitudinal axis of a cylindrical coordinate systemwith the symmetry point in the previous layer n.

FIG. 18c is a top-down illustration of a successive layer n+2, relativeto layer n+1 and layer n described in FIG. 18b . and FIG. 18a ,respectively, of a circular scan strategy implementation of the coveringproblem solution unit cell as described in FIG. 16. Scan paths arecylindrically symmetric to the previous layers n and n+1 with AM trackgeometry parameters assigned consistent with layer n and alternatelyrelative to layer n+1.

FIG. 18d is a path-tangent cross-sectional illustration of the threesuccessive layers (layer n, n+1, n+2 as described in FIG. 18a-c ) alongthe section line indicated in FIG. 18c , showing the application of thecovering problem solution shown in FIG. 16, through the rotation of theunit cell about the longitudinal axis of a cylindrical coordinatesystem. It is of note, however, that the scan paths need not becircularly symmetric about a longitudinal axis but the symmetry pointcould be translated between layers and might be advisable due to thesmall variations in height at the surface of the scan tracks printed ineach layer. Furthermore, the scan paths could be drawn along anarbitrary contour provided the paths are nearly parallel.

FIG. 19 is an illustration of scan tracks in a scan strategy with arotation of about 90 degrees every two layers derived from the coveringproblem solution depicted in FIG. 7b . The rotation angle shown is about90 degrees, but it could be chosen to suit desired printed articleproperties, or to improve throughput at a given porosity, or for otherreasons. Additionally, rotation need not occur every two layers, butcould occur every layer, or every n layers. Further, the tracks need notbe straight within each layer as shown for simplicity of representationin this figure, but could consist of parallel paths of any directionalong the surface of the layer.

FIG. 20a is an illustration depicting scaling performed on the unit cellfrom the covering problem solution shown in FIG. 7, whereby this scaling(and other operations) permit degrees of control over the scan paths andtherefore the speed of print (printer throughput) and physicalproperties and qualities of the printed article, measured, by way ofexample, in terms of article porosity. The unit cell is scaled down inthe hatch spacing direction, accomplished by reducing the hatch spacingwhile holding AM track geometry parameters fixed. This is a conformal(angle preserving) scaling in the unit cell by a factor of 0.87 in thex-direction (right), meaning that the angle between the centers of theobjects changes, as well as the ratios between slice thickness to hatchspacing, and slice thickness to track width, assuming constant slicethickness similar to those presented in FIG. 15. Other scaling anddistortion operations are of course also possible. In general,increasing the degree of overlap of tracks as compared to the tracksdepicted in FIG. 7b in a binder jetting, powder bed fusion, lasersintering, or similar process will decrease the porosity of the printedarticle and the speed of print, up to a point, and then porosity maybegin to increase once again. In a material jetting, fused depositionmodeling, or similar process, a slight decrease in track overlap ascompared to that in the tracks depicted in FIG. 7b might be required toreduce porosity, but as overlap was decreased further and eventuallyeliminated entirely, porosity would increase.

FIG. 20b is an illustration for the unit cell depicted in FIG. 20adepicting a change in AM track geometry parameters designed to increaseoverlap, as might be useful in decreasing the porosity of an articleprinted by a binder jetting, powder bed fusion, laser sintering, orsimilar process. In this example, print speed (an AM track geometryparameter) is reduced for the smaller objects, resulting in 17.5% deeperand wider such objects for a total area increase of 38%, and thesesmaller objects are additionally relocated somewhat lower in the cell tomore accurately reflect track fabrication given a slower speed of print.Other such AM track geometry parameter changes (and position changes)can be applied in general in a similar fashion to increase or decreaseporosity, print throughput, and other printed article and printingcharacteristics. The unit cell depicted in this figure, contains slicesand scan paths defined perpendicular to the plane of the layers as inFIG. 7d and rotation every two layers as in FIG. 19.

FIG. 21 is an illustration of a cross section of an article with thenormal of the sectioning plane in a path-tangent direction, where thearticle is printed according to a covering problem solution derivedusing unit cells on curved and scaled space with spherical geometry,employing a material jetting, fused deposition modeling, arc plasmasintering, multi-jet fusion, binder jetting or similar process. Inparticular, the unit cell and the positions of the objects depicted inFIG. 7b are scaled by the transformation: z->r, x->0, for radialcoordinate r representing a distance r from a center point and angle θ arotation from zero degrees at radius r, and where the width w of thecell in x-z space is taken to be equal to the width of the cell at layerone in the image, meaning w²=2*(r₁)²*cos(θ)) at layer one. In thistransformation, each unit cell increases in area (or volume) as theradial distance from the center point is increased, and the centerposition of each track is also according scaled; however, the trackcross sections are not scaled, suggesting no change to AM track geometryparameters. To account for distortions due to scaling, tracks size mightbe scaled as well according to the radial distance by altering AM trackgeometry parameters; or, every few layers, unit cells could be downsizedsuch that at layer n, w²=2*(r_(n))²*(1−cos(θ)). The labels “1.1” aremeant to indicate that these tracks are printed first, with tracks “1.2”printed subsequently to achieve higher maximal radial build-up based onthe surface structure of the tracks printed in the prior layer. Trackheight follows the arc of the sphere's surface in the build-updirection, perpendicular to the surface of a sphere of radius r, butscan paths might travel according to curved or straight contours, by wayof example, around an axis through the center point to its highest pointin the figure, or in a straight line into the page. Material thickness(MT) and net displacement (ND) need not be equal nor consistent betweenlayers. In this example, MT₃>ND₃>MT₄>ND₄.

FIG. 22 is an image of a path-tangent track cross section of a singlelayer of a stainless steel part printed by laser powder bed fusion witha laser power of 250 W, hatch spacing of 140 um, gaussian beam waist of55 um and laser scanning speed of 1046 mm/s. This single layer isrepresentative of a single layer in a single track geometry scanstrategy; typical in such strategies, scan path directions in successivelayers will be rotated relative to previous layers, though this is notshown here.

FIG. 23 is an image of a path-tangent track cross section of two layersof a stainless steel part printed by laser powder bed fusion with alaser power of 250 W, hatch spacing of 140 um, gaussian beam waist of 55um, and laser scanning speed of 1210 mm/s. This is an implementation ofthe specific “interleaved” scan strategy described in U.S. Pat. Nos.6,596,224 and 6,677,554 and diagrammed in FIG. 4. Note how thepath-tangent cross section of each scan track is similar between the toplayer (second layer) and the layer below (first layer). It is of notethat the area of the track cross sections of the first layer that arecovered by the track cross sections of the second layer are no longervisible; this is a common feature of cross-sectional images where trackoverlap occurs.

FIG. 24 is an image of a path-tangent track cross section of a singlelayer of a stainless steel part printed by laser powder bed fusion basedon the covering problem solution detailed in FIG. 16. In this case,track cross sections of two different areas/geometries are achievedutilizing different scan strategies. Small width tracks are printed witha laser power of 250 W, gaussian beam waist of 55 um, and laser scanningspeed of 2038mm/s, while large width tracks are printed with a laserpower of 250 W, gaussian beam waist of 55 um, and laser scanning speedof 860 mm/s, where the distance between the centers of small and largetracks is fixed at 140 um.

FIG. 25 is an image of the path-tangent track cross section of twolayers of a stainless steel part printed by laser powder bed fusionbased on a covering problem solution utilizing two track geometries. Inthis example, an initial layer of large width scan tracks separated by140 um hatch spacing are printed from 50 um powder thickness with alaser power of 250 W, and gaussian beam waist of 55 um. A second layerwith net displacement and powder thickness of 50 um is employed toproduce small width scan tracks whose track cross section center pointsare displaced approximately 70 um relative to the large width scan trackcross section center points of the first layer; the same parameters areused except with scan faster by a factor of 1.6.

FIG. 26 is an image of a track cross section, with unit normal tangentto half of the scan tracks and perpendicular to the other half, of apart printed in stainless steel by laser powder bed fusion employing aniteration of the two track geometry approach described for FIG. 25. Inthis case, after producing the two layers as described in FIG. 25, scantracks are rotated 90 degrees to produce the next two layers, again inthe same fashion again as shown in FIG. 25. This two layer build plus 90degree rotation is repeated as often as required.

FIG. 27a is an image of track cross sections, taken 45 degrees off ofunit normal, of a part printed in an aluminum alloy with a two trackgeometry scan strategy similar to that described for FIG. 26, except inthis case with 375 W laser power and hatch spacing of 220 um, where thesmaller tracks are printed employing a smaller beam waist and fasterscan speed relative to the larger tracks.

FIG. 27b is an image of track cross sections, taken 45 degrees off ofunit normal, of a part printed in an aluminum alloy with a single trackscan strategy employing 375 W laser power, a gaussian beam waist of 46um, 220 um hatch spacing, and scan speed of 1311mm/s. In this strategy,scan paths are rotated by 90 degrees every layer.

FIG. 28a is a cross sectional image of a part printed in nickelsuperalloy by laser powder bed fusion employing a similar two track scanstrategy as to that described for FIG. 26. In this case, a laser powerof 269 W, hatch spacing of 140 um, a net displacement and powderthickness of 50 um, and a gaussian beam waist of 55 um were employed,where the scanning speed used to fabricate the larger tracks was twicethat of the speed used to generate the smaller tracks. Measured porosityfor this part was 0.12%, far lower than that measured for the partsshown in FIGS. 28b and 28c , which were printed using the same totaldeposited energy per unit mass as the part shown here.

FIG. 28b is a cross sectional image of a part printed in nickelsuperalloy by laser powder bed fusion employing a one track“interleaved” scan strategy similar to that described for FIG. 23. Inthis case, a laser power of 269 W, hatch spacing of 140 um, a netdisplacement and powder thickness of 50 um, and a gaussian beam waist of55 um were used to generate the tracks, where the total deposited energyper unit mass was the same as for those parts shown in FIGS. 28a and 28c. Measured porosity for this part was 0.50%, lower than that measuredfor the part shown in FIG. 28c but far higher than that measured for thepart shown in FIG. 28a .

FIG. 28c is a cross sectional image of a part printed in nickelsuperalloy by laser powder bed fusion employing a one track scanstrategy similar to that described for FIG. 8. In this case, a laserpower of 269 W, hatch spacing of 140 um, a net displacement and powderthickness of 50 um, and a gaussian beam waist of 55 um were used togenerate the tracks, where the total deposited energy per unit mass wasthe same as for those parts shown in FIGS. 28a and 28b . Measuredporosity for this part was 0.69%, higher than that measured for theparts shown in both FIGS. 28a and 28 b.

FIG. 29a is an illustration of a unit cell consisting of three differentobject geometries generated from different AM track geometry parametersmost consistent with powder bed fusion, laser sintering, or a binderjetting printing process. In this case, one large, two medium, and threesmall objects are present in each unit cell, and this is the minimumbasis possible. Several slice thicknesses are possible for thisconfiguration; consequently, the basis vectors (b₁,b₂) are given interms of the length of the x-axis parallel vector as (1.0, 0.0), (0.44,1.03). The x-axis is directed to the right, and the z-axis upwards.

FIG. 29b is an illustration of a single layer onto which material forthe successive layer has been deposited, where the net displacement ND₂in this case is less than the material thickness MT₂ for this slice. Thescan strategy employed is designed from a covering problem solutionemploying multiple track object geometries and sizes as shown in FIG.29a , and includes alternating order of track printing, different netdisplacements between slices, and multiple material thicknesses that areeither greater than or equal to the net displacement within a singleslice, depending on the slice. The labels “1.1” are meant to indicatethat the smaller tracks are printed first, with the larger tracks,labeled “1.2”, immediately after. This strategy could be applied, withsome modification, in any printing process, but track cross sectiongeometry is in this case drawn to reflect tracks generated employing AMtrack geometry parameters for a powder bed fusion, laser sintering, orbinder jetting process, where for the latter case a scaling-up of theunit cell beyond what is depicted in this FIG. 32 ight be advantageousin preventing overdeposition of binder.

FIG. 29c is an illustration of the layer printed after the deposition ofmaterial shown in FIG. 29b , and the deposition of material for theprinting of the next layer. In this case, the smaller tracks (labeled“2.1”) are printed first, then then larger tracks (labeled 2.2). For thenext layer, the material thickness MT₃ and the net displacement ND₃ arethe same.

FIG. 29d is an illustration of the layer printed after the deposition ofmaterial shown in FIG. 29c . As in previous layers in this example, thesmaller tracks (labeled “3.1”) are printed before the larger tracks(labeled “3.2”). For articles fabricated this strategy, the x-axiscomponent of the shear strength would be increased relative to a scanstrategy with tracks laid one on top of the other due to the largez-axis span of tracks both within layer and across layers. This strategymight be well-suited to binder jetting, with the order of printingsmaller and larger objects within each layer reversed, where higheryield strength was desired along the direction of scanning (into thepage) and relatively higher shear strength was desired in and about thex-axis. Incorporating rotations every other layer would increase yieldstrength and shear strength in the x-axis direction while decreasingyield strength in the direction of scanning.

FIG. 30a is a cross sectional image of a part printed in stainless steelby laser powder bed fusion employing a one track scan strategy similarto that described for FIG. 8. In this case, a laser power of 260 W,hatch spacing of 140 um, a net displacement and powder thickness of 50um, a gaussian beam waist of 91 um, and a scan speed of 1004 mm/s wereused to generate the tracks. Measured porosity for this part was 0.48%,higher than that measured for the part shown in FIG. 30 b.

FIG. 30b is a cross sectional image of a part printed in stainless steelby laser powder bed fusion employing a one track scan strategy similarto that described for FIG. 8. In this case, a laser power of 260 W,hatch spacing of 140 um, a net displacement of 50 um, a powder thicknessof 60 um, a gaussian beam waist of 91 um, and a scan speed of 1004 mm/swere used to generate the tracks. Measured porosity for this part was0.21%, considerably lower than that measured for the part shown in FIG.30a . The decrease in porosity is attributable to the increase in powderthickness relative to net displacement.

FIG. 31a is a cross sectional image of a part printed in an aluminumalloy by laser powder bed fusion employing a similar two track scanstrategy as to that described for FIG. 27. In this case, a laser powerof 650 W, hatch spacing of 200 um, and a net displacement and powderthickness of 50 um were employed, where the scanning speed used tofabricate the larger tracks was about 1.9 times that of the speed usedto generate the smaller tracks, and the gaussian beam waste used togenerate the larger tracks was about twice the size of that used togenerate the smaller tracks. Measured porosity for this part was 3.29%,far higher than that measured for the part shown in FIG. 31b , which wasprinted using the same total deposited energy per unit mass as the partshown here.

FIG. 31b is a cross sectional image of a part printed in an aluminumalloy by laser powder bed fusion employing a similar two track scanstrategy as to that described for FIG. 31a . In this case, thedifference between strategies was that for this part, a powder thicknessof 60 um rather than 50 um was applied. Measured porosity for this partwas 1.79%, considerably lower than that measured for the part shown inFIG. 31a . The decrease in porosity is attributable to the increase inpowder thickness relative to net displacement.

FIG. 32a is a cross sectional image of a part printed in stainless steelby laser powder bed fusion employing a similar two track scan strategyas to that described for FIG. 26. In this case, a laser power of 252 W,hatch spacing of 140 um, a net displacement and powder thickness of 50um, and a gaussian beam waist of 55 um were employed, where the scanningspeed used to fabricate the larger tracks was about 1.6 times that ofthe speed used to generate the smaller tracks. Measured porosity forthis part was 0.23%, far lower than that measured for the parts shown inFIGS. 32b and 32c , which were printed using the same total depositedenergy per unit mass as the part shown here.

FIG. 32b is a cross sectional image of a part printed in stainless steelby laser powder bed fusion employing a one track “interleaved” scanstrategy similar to that described for FIG. 23. In this case, a laserpower of 252 W, hatch spacing of 140 um, a net displacement and powderthickness of 50 um, and a gaussian beam waist of 55 um were used togenerate the tracks, where the total deposited energy per unit mass wasthe same as for those parts shown in FIGS. 32a and 32 c. Measuredporosity for this part was 0.56%, lower than that measured for the partshown in FIG. 32c but far higher than that measured for the part shownin FIG. 32 a.

FIG. 32c is a cross sectional image of a part printed in stainless steelby laser powder bed fusion employing a one track scan strategy similarto that described for FIG. 8. In this case, a laser power of 252 W,hatch spacing of 140 um, a net displacement and powder thickness of 50um, and a gaussian beam waist of 55 um were used to generate the tracks,where the total deposited energy per unit mass was the same as for thoseparts shown in FIGS. 32a and 32b . Measured porosity for this part was1.13%, much higher than that measured for the parts shown in both FIGS.32a and 32 b.

DESCRIPTION OF THE INVENTION

Systems, processes, and compositions of matter are described that employthe principal of varying track and track cross section shape, size, andposition within a single layer and across different layers in order toincrease printer speed and throughput (decrease print cost), to decreasefabricated article porosity, to improve fabricated article strength andother desirable physical characteristics, and to improve printreproducibility. Additionally, systems and processes are described inwhich material thickness and net displacement are individuallycontrolled and are made to differ over single or multiple layers,resulting in changes to track and track cross section shape, size, andposition, in order to increase printer speed and throughput (decreaseprint cost), to decrease fabricated article porosity, to improvefabricated article strength and other desirable physicalcharacteristics, and to improve print reproducibility. The inventionscontemplated herein are applicable for any AM or 3D printing processwhere a track of material and/or scan path is generated or employed, orwhere surface height variations are produced in a layer-wise fashionthat are similar to those exhibited by a series of tracks, including butnot limited to fused deposition modeling, material jetting, binderjetting, powder bed fusion, selective laser sintering, multi-jet fusion,directed energy deposition, direct metal deposition, electron beamadditive manufacturing, arc plasma sintering additive manufacturing, andthe applicability of the inventions contemplated herein is not limitedto a single or to a small number of materials employed in theaforementioned track and scan path based printing processes and printersand for those processes and printers producing similar layer-wisesurface variations; rather, the inventions are expected to beadvantageous in the use of all or nearly all such materials, includingin the use of composite materials and multi-material printing.

The benefit of the inventions described herein are obtained by alteringAM track geometry parameters {P} and feedstock parameters {f} in orderto implement targeted scan strategies and material deposition methodsthat are more efficient in deposited energy usage and/or time ofmaterial deposition, curing, melting, bonding, hardening, sintering, orfusing than other methods, and that generate compositions linked tothose strategies with advantageous physical properties including but notlimited to increased ductility, strength, isotropy (or anisotropy),fatigue resistance, thermal conductivity, electrical conductivity,surface roughness, and others. AM track geometry parameters {P} includebut are not limited to; scan speed of energy deposition along track pathor scan speed of material- and/or energy-depositing print head, totalamount of energy deposited per unit time or total mass of materialdeposited per unit time, average slope of the surface upon which a scantrack is being produced, parameters controlling powder or materialthickness and volume of material deposited, net displacement, parameterscontrolling compaction of material, area of space over which energy ormaterial is deposited when producing a track, shape of the space overwhich energy or material is deposited or shape of the nozzle,temperature of the area or build platform over which printing isoccurring, temperature to which feedstock material is heated beforedeposition, velocity of gas flow over the surface of the build, and manyothers. Feedstock parameters {f} include but are not limited to;temperature-dependent viscosities of materials, melting temperature ofmaterials, flow characteristics of materials (e.g., shear thinning ofshear thickening), packing fraction of material in powder form (tappacking fractions and others), loading of particles in suspension,particle sizes, shapes and surface roughnesses for powders and particlesuspensions, specific heat of materials, plasticity of materials, andmany others.

Critically, the scan paths describing the motion of the energydeposition or of material or energy-depositing print head, including thelocal curvature or angle of the tracks (both relative to prior andsuccessive layers and relative to a global coordinate system), the orderin which tracks are printed, the hatch spacing, and related directionalvariables, are not included in the set of AM track geometry parameters{P} or feedstock parameters {f}. This is because these components do nottend to change track (or track cross section) geometry parameters much,but are rather indicators of where tracks will be fabricated. It is ofnote that in some printing processes, including but not limited topowder bed fusion and selective laser sintering, hatch spacing and theorder of track printing within a layer in particular can have someeffect on track geometry due to the creation of denudation zones andother phenomena; however, in general, changes in these parameters overthe phase space of filling hatches tend to elicit relatively small, ifmeasurable within error, changes in track geometry.

Summary of select distinctions from prior art. The followingdistinctions are not meant to be an exhaustive list, but rather asummary of a few important contrasts distinguishing this invention fromprior art.

Additive manufacturing that employs track-based geometries is almostalways conducted on a layer-by-layer basis, where scan strategies withinany given layer are designed in order to produce desirable physical andgeometric properties for that layer rather than designed in concert withdesigning the strategies for prior or successive layers, except insofaras global rotations of path direction or paths near article edges areconsidered. Even in the case of print lattices, the scan strategiesemployed to fabricate the struts and nodes are generally formulated withinput only from data concerning the layer in question, rather than withinformation about scan strategies in prior or successive layers. Thisapproach, among other benefits, provides the opportunity for parallelcomputation (where each layer's scan paths are computed simultaneously)in computer-generation of scan strategies.

The interleaved layer filling strategy discussed in U.S. Pat. Nos.6,596,224 and 6,677,554 is an exception, in that the direction of scanpaths in this strategy in layer n is the same as the paths in either theprior (n−1) or subsequent (n+1) layer, and the positioning of the pathsin layer n is halfway between that of the paths in either the prior orsubsequent layer, as illustrated in FIG. 4. In this case, however, as inother cases, multiple AM track geometry parameters are not employedwithin the same filling strategy; rather, the same AM track geometryparameters are employed across a plurality of layers, even though theposition of scan paths in each layer is dependent on the paths in thelayer above or below.

From a crystallographic perspective, scan strategies employing a singleset of AM track geometry parameters consist of the periodic replicationof a unit cell with only one object contained within. Such strategiescan be described mathematically by a lattice with a basis of one. In twodimensions, it is well-known to those knowledgeable in crystallographythat there are only five families of such lattices, and in threedimensions only fourteen. In the inventions concerning covering and scanstrategies discussed within this patent, any scan strategy or printedcomposition that can be described, in terms of a basis of AM trackgeometry parameters, by a lattice with basis one, is excluded; rather,the inventions require the application of different AM track geometryparameters within the same strategy, therefore requiring a unit cellwith a basis greater than one.

Specifically, the methods and compositions inventions concerningcovering and scan strategies require within a strategy that: 1) thetracks or track cross sections employ different AM track geometryparameters, thereby usually generating different track geometries,either within a single layer or across a plurality of successive layers,2) the tracks or track cross sections can be characterized, according totheir associated AM track geometry parameters or track geometries, by aunit cell, described in Euclidean or other geometric space, with a basisof no less than two, 3) where the printed tracks within the unit cellcover the space of the cell in the sense that no areas (volumes) ofunprinted material are present larger than the largest track crosssection (track), and 4) where portions of or all of at least twoadjacent unit cells are present in each layer in regions to which thestrategy is applied.

The requirement for the presence of elements of at least two adjacentunit cells is meant to exclude printing where different single-basislattice strategies are applied to different regions within a layer oracross layers. Prior art demonstrates that different scan strategies areoften applied to different regions within a layer, for example, where aprint lattice strategy is employed in the center of the layer, where acontour scan strategy is employed on the outer edge of the layer, and afilling strategy is employed in between. One could describe that layeror a substantial portion of it and any similar prior or successivelayers by a single unit cell with a large basis; however, elements of atleast two such cells would not be present within each layer. Therestrictions requiring that the tracks within a unit cell form acohesive solid within the region of the cell, without unprinted materialof the size of the largest track or larger, are intended to exclude unitcells in print lattices or similar periodic structures where much or amajority of the material is unprinted. Roughly put, the inventions applyto filling strategies, including the filling of contours that consist ofmultiple adjacent scan tracks, print lattices with struts that are notcomposed of single scan lines, skins, and other such printed structures.

Additionally, the inventions concerning covering and scan strategiesinclude the cases where a non-periodic or quasi-crystalline applicationof AM track geometry parameters, applied either in the form of theprinting parameters or the placement of tracks in space, is employedwithin a filled region of printed space.

With respect to layer thickness, prior-art does not distinguish betweenslice thickness, material thickness, and net displacement, and whereobservations (if any) are made toward such a distinction, they areviewed as negatively or neutrally impacting fabricated article quality,printer speed, or other print or article characteristics. The inventionsdiscussed herein describe a view of additive manufacturing in whichthese concepts are considered different and a method of fabricatinglayers where some or all of these three are intentionally andcontrollably made to differ from one another, in many cases producingresults advantageous to printing. In particular, material thickness andnet displacement are introduced as independent AM track geometryparameters, and the modification of these parameters independently viathe methods discussed herein produce results advantageous to printing.

Scan paths derived from a plurality of track cross section shapes and/orsizes. When considering the melting, sintering, fusing, or otherwisebinding (hereafter all included in the terms “fusing” or “fused”, unlessotherwise specified) of powder particles to one another and whenconsidering the solidification or hardening (also referred to as“fusing” or “fused”, for the sake of simplicity, unless otherwisespecified) of a suspension, slurry, liquid, gel, curable polymer orother medium (hereafter all included in the term “slurry”, unlessotherwise specified) due to targeted energy, binding agent, or materialdeposition, re-melting, re-sintering, re-fusing, or re-binding(hereafter all included in the terms “re-fusing” or “re-fused”, unlessotherwise specified) of particles or slurry melted during the processingof a preceding slice is necessary to fabricate articles of low porosity,and to ensure that pockets of unmelted, unsintered, unfused, unhardened,unsolidified, or unbound (“hereafter all included in the terms“unfused”, unless otherwise specified) particles or slurry does notremain after printing. There are at least two general reasons for thisrequirement. The first is that a scan or track based print processgenerally creates tracks that do not tile space, meaning that any scanstrategy that did not employ sufficiently overlapping tracks, whereoverlapping tracks result in re-fusing in the regions of intersection ofa plurality of tracks, would result in unfused particle or slurry, orpockets devoid or partially depleted of particles or slurry, in thespaces between tracks. The second general reason is that scan and trackbased printing produces tracks that vary stochastically in their localgeometry, meaning that there is substantial variation in track width,height, depth, and surface structure over the length of a track, wherethe degree of stochastic variation is dependent on controlled variablessuch as the print process employed, printing parameters, feedstockparameters, and other variables, as well as uncontrolled variables.Consequently, if a scan strategy is not designed with sufficientoverlap, then in the neighborhood of the border of a track at certainpoints along track length, local variation in track geometry will resultin a lack of particle or slurry fusing.

Overlap is necessary to reduce the volume of space in an article inwhich there is a lack of fusing, and it is necessary to produce lowporosity and nearly-porosity-free parts. However, overlap isinefficient, in that energy or time is committed to re-fusing particlesor slurry that were previously fused. Therefore, scan strategies thatreduce or eliminate areas of overlap where those areas are not needed toensure the fusing of particles or slurry (termed excess overlap) aremore efficient in terms of the use of energy and time. Generallyspeaking, employing scan strategies that involve tracks or track crosssections of different geometry (size, shape, surface properties) allowsfor the reduction of excess overlap compared to what is possible withtracks or track cross sections of only one geometry.

It is important to note that neither the average geometry nor theaverage volume of fused track produced, considering the space of AMtrack geometry parameters and feedstock material (powder or slurry), isgenerally precisely linearly dependent on the amount of energy or timespent producing the track. It can be useful therefore to define for eachprinter a set of scalar track efficiency functions {T_(j)(P^(j))}, inunits of track volume printed per unit time, track volume printed perunit energy, track cross section area printed per unit time, or trackcross section area printed per unit volume, where a set of differentfunctions exists for each printer in terms of the feedstock material(powder or slurry), indexed “j”, and dependent on a feedstock-specificnumber “I_(j)” of AM track geometry parameters {P^(j) _(i)}, i=1 . . .I_(j), specific to that printers capabilities and the feedstock. Moregenerally, size characteristics representing the geometric shape of atrack or track cross section can be defined for a given a set of printerhardware and feedstock material, where these characteristics are alsodependent on AM track geometry parameters. An example of sizecharacteristic functional definition can be found in the journalarticle: C. Kamath, B. El-dasher, G. F. Gallegos, and W. E. King, and A.Sisto, Density of additively-manufactured, 316L SS parts using laserpowder-bed fusion at powers up to 400 W, Int. J. of Adv. Manuf. Technol.74, pp. 65-78, 2014, where 316 Stainless Steel tracks are producedaccording to varying the AM track geometry parameters laser speed andlaser power, with fixed other parameters such as a layer thickness of 30microns and a laser spot size of about 63 microns, and where trackheight, track width, and track depth are measured in terms of the twovariable parameters.

Employing the above-described AM track geometry parameter dependentefficiency function, single or multilayer scan strategies depicted inthree dimensions in terms of overlapping tracks or in two dimensions interms of track cross sections may be directly compared on the basis ofenergy or time efficiency. Additionally, because excess overlap isundesirable in efficiency terms, given a specific set of printerhardware, feedstock material, and AM track geometry parameters thatproduce one or more track geometries, better covering problem solutionsfor those track geometries will tend to be representative of more timeand energy efficient scan strategies. Further, insofar as a family ofdenser packings of objects of the same or similar geometry to suchtracks can be used to generate covering problem solutions, the densityof such packings will tend to correlate positively with the time andenergy efficiency of scan strategies generated from them. FIG. 7illustrates an example of an efficient scan strategy based on a coveringproblem solution derived from a dense binary packing of disks. In thisexample, the objects' track cross sections are approximations of trackcross sections produced using laser powder bed fusion.

For a given printer, considering “J” feedstocks (where the integer J>1for multi-feedstock or multi-material printing) and for each a number“K_(j)” of parameter sets {P^(j) _(i)}_(k), k=1 . . . K_(j), thefunction values T_(j)({P^(j) _(i)}_(k)) can be used as weights in acovering problem posed in a variable unit cell with lattice basisvectors b and volume v_(U)(b), and a basis of objects numbering ΣK_(j)tracks or track cross sections (where the sum Σ runs j=1 . . . J), andin which each track or track cross section object exhibits geometrycorresponding to its parameters {P^(j) _(i)}_(k). Labeling each objectO_(j,k) by its feedstock index “j” and parameter set index “k”, aconfigurational coordinate r_(j,k) and area or volume v_(j,k) for thatobject can be defined, where most simply the position components of theconfiguration r_(j,k) would correspond with the scan path of thematerial- and/or energy-depositing print head or other AM printermaterial or energy source. The weighted covering problem may be writtenas a constrained optimization problem with objective:

$\min \frac{1}{\underset{\{ r_{j,k}\}}{v_{U}}(b)}{\sum\limits_{j,k}{{T_{j}\left( \left\{ P_{i}^{j} \right\}_{k} \right)}v_{j,k}}}$

where the minimization of the objective function over the objectconfigurations r_(j,k) and basis vectors b is subject to the constraintthat the entire volume of the unit cell defined by basis vectors b iscovered by the objects O_(j,k). The covering might also be a double,triple, or greater multiple covering where the unit cell is covered anintegral number of times by the objects, and other constraints could beplaced as well. By way of example, it might be that the precise geometry(and area or volume v_(j,k)) of the objects is somewhat dependent on theother parameters {P^(j)}_(k) of the other objects in the unit cell, oreven their relative configurations; if any such configuration dependenceis known, it might be advantageous to constrain object configurations tothe phase space for which it is known. It is important to note, however,that knowledge of any relative configurational dependencies (or otherdependencies) is not necessary for the development of viable scanstrategies, even though in some cases such knowledge might result inscan strategy improvements.

It is sometimes advantageous to measure average track geometry for agiven feedstock in an environment that is similar to actual printconditions. This approach may include but is not limited to: a)including in the measurement of average track geometry those tracks thatare printed on top of other tracks, rather than tracks where material isdeposited on a smooth surface, b) if multiple feedstocks are to beemployed in a print, generating tracks of each individual feedstockprinted on layers composed of relative compositions in ranges similar tothose targeted in the printed article, thereby printing in conditions ofelastic stress, thermal conductivity, and where applicable, electricalconductivity and other physical properties, are similar to those in theprinted articles, c) where the order of printing of tracks might not bechronological according to adjacent tracks, measuring average trackgeometry according to the ordering to be used, and d) where tracks ofdiffering average geometry are to be present in the printed article,measuring the geometry of each set of tracks produced with a given setof track geometry parameters {P^(j)}k in proximity to those of othertracks (with differing “j” or “k” index) in a fashion as similar toprojected printed article conditions as reasonably possible.

By way of example, when considering the two track geometriescorresponding to the path-tangent track cross sections depicted in theunit cell shown in FIG. 7, it might be advantageous to measure theaverage geometry of the larger tracks by printing those tracks on top ofa layer (or more than one layer) of the smaller tracks, and vice versa.This could be particularly relevant in a powder bed fusion or selectivelaser sintering process; if during the printing of a layer n thematerial is not fully melted, as seen for example in FIG. 7d wherepowder remains between the path-tangent cross sections depicted, thatremaining material may nonetheless have been sintered or partiallysintered, thereby changing the physical properties of the material andconsequently possibly the track geometry of the tracks in layer n+1.This could also be the case if nearest-neighbor tracks were not printedin sequential order, but instead in even-odd parity (“every othertrack”), or other ordering. By way of example for general printingprocesses, the shape of the track can depend on the surface upon whichthe material is deposited, and in the example in FIG. 7, the surfaces ofthe smaller and larger tracks are different, thereby potentiallyaltering the geometry of tracks printed on those surfaces and furtheraltering the tracks in successive layers.

It is important to note that in processes where material is deposited intracks such as material jetting, fused deposition modeling, multi-jetfusion, arc plasma sintering, some binder jetting processes and similarprocesses, the geometry of a track in a printed article may in somecases depend heavily on the surface on which the track is printed, wherethat surface often includes fully or nearly solidified, hardened orcured material from printing of tracks in prior layers. In the case ofbinder jetting or similar processes where a slurry, liquid, solvent,polymer, suspension, or other material in a flowable state, throughcapillary and deposition forces, infiltrates a layer of particulates toform a track consisting of both the material jetted and theparticulates, the bottom shape of a track printed on top of previouslysolidified, hardened, or cured material from previously printed tracksmay conform to the top of the previously printed tracks. Such a trackshape differs substantially from a track printed with the same AM trackgeometry parameters, but on a deep (relative to track height) layer ofparticulate, or a thinner layer of particulate on top of a flatsubstrate. In a material jetting, multi-jet fusion, arc plasmasintering, fused deposition modeling, or similar process, the geometryof the surface on which the track is printed can also have an effect ontrack shape; in these cases, the extent of the effect is dependent onthe viscosity of the material printed as compared to its curing, drying,or hardening time, in that a fast-hardening material with high viscositywill maintain a more independent geometry, whereas a slow-hardeningmaterial with low viscosity will tend to conform to the shape of thesurface below it.

Regardless, the overlapping covering problem solutions described, forexample in FIG. 7, with track geometry derived from printing onparticulate layers (binder jetting) or relatively smooth surfaces(material jetting, multi-jet fusion, arc plasma sintering, fuseddeposition modeling), can be employed in these material depositionmethods to advantageous effect. The reason is that the volume of aprinted track will remain roughly constant, dependent almost entirely onAM track geometry parameters, regardless of the geometry of the surfaceon which the track is printed, even if track shape changes. Therefore,the ratio for tracks (track cross sections) of overlap volume (area) tototal volume (area) in a covering problem solution unit cell, for theseprinting processes, can be taken as a measure of how much excesssolution including binder and/or material it is necessary to deposit tofill the space of the cell without voids.

Capillary and deposition forces during track deposition will allowfilling of some of the space between tracks printed previously, but asmentioned previously, the bottoms of printed tracks do not completelyconform to the surfaces on which they are printed. Consequently, designof scan tracks using good covering problem solutions that employoverlap, but not too much (excess) overlap, between tracks will stilltend to result in either a larger ratio of particles (for example,powder) to solution in green articles with very low porosity in binderjetting and similar processes, and a reduction in void space in materialjetting, fused deposition modeling, arc plasma sintering, multi-jetfusion, and similar processes.

Elaborating, in binder jetting, enough solution including binding agentmust be deposited to fill some, but not necessarily all, of the spacebetween particles, where the quantity of solution deposited for a trackof given geometry might be made directly proportional to the volume(surface area) of the track (track cross section) in a covering problemsolution. However, excess solution, in addition to potentially causingproblems during any binder removal step that is part of the sinteringprocess, will lower the density of particulates in the green article andtherefore either increase shrinkage during sintering or increase theporosity of the sintered part. Consequently, though scan strategies thatemploy overlap are necessary to ensure that the space between particlesis sufficiently filled (for the reasons discussed previously), scanstrategies designed from good covering problem solutions can reduce theminimal necessary overlap, thereby reducing part shrinkage duringsintering and/or sintered part porosity. In material jetting, fuseddeposition modeling, multi-jet fusion, arc plasma sintering, and similarprocesses, overlap is again required, in this case to help ensure areduction in voids in a printed article (both green and, where part ofthe process, sintered), but excess overlap can lead to over-depositionof material and/or other problems similar to those described for binderjetting.

A good example of the types of problems that can emerge when excessoverlap is employed in the generation or use of the scan strategy can beseen in FIGS. 8 and 9. FIG. 8 is a cross-sectional image of a cubeprinted using a material jetting process (fused deposition modeling)employing a thermoplastic polymer whereby tracks of a single geometry inlayer n are laid down side by side with 400 um spacing, and in layern+1, the same approach and track geometry are employed but tracks arerotated 90 degrees relative to layer n. FIG. 8 is an image of a partprinted with machine nozzle speed, temperature, and material extrusionrate, among other parameters, optimized to print parts without creatingmechanical problems in the printer, to generate a geometricallyrelatively more accurate part, and to minimize surface roughness, amongother factors. For these settings, the resulting printed cube exhibitsroughly 8% porosity. FIG. 9 is a cross-sectional image of the samedigital cube (the image is rotated 90 degrees relative to FIG. 8) butprinted with one setting change: an increase in the volume of materialextruded, leading to larger, sometimes non-cylindrical, tracks. Theprint failed in the sense that the nozzle began scraping against thepart due to an overabundance of material extruded, which can be viewedfrom a covering problem perspective as excess, or “too much” overlap.The edges and surface of the part were also far out of specificationfrom a geometric perspective and from the perspective of surfaceroughness, as can be seen in FIG. 9, and the part exhibited porositiesaveraging 7% away from its edges.

Such problems are alleviated when scan tracks of multiple geometries areemployed, as is described in Examples 1 and 2. Using the same printparameters as in FIG. 9 except employing scan strategies utilizing twotrack geometries, substantially decreased porosity can be achievedwithout a failed print, loss of geometric tolerance, or increase insurface roughness. FIGS. 10 and 11, discussed in Examples 1 and 2, arecross-sectional images of the same digital cubes as shown in FIGS. 8 and9, except printed with two different scan strategies each employing twotrack geometries. The tracks shown in FIG. 12 are representative of thetrack geometries deployed in FIGS. 10 and 11 (though in FIG. 12, thevolume extrusion rate of material for each type of track has been scaleddownwards proportionally so as to generate an image where trackgeometries are clearly discernable). The porosities measured for thecubes shown in FIGS. 10 and 11 are 0.2% and 2.3%, respectively, and thegeometrical accuracy of the cube relative to the digital image, as wellas the surface roughness, are improved as compared to the 8% porositycube shown in FIG. 8, clearly demonstrating the advantages of themultiple track geometry methods employed.

The covering optimization problem thus far discussed may be extended,including by way of example such that object shape and size, which areAM track geometry parameter dependent, are variable rather than fixed,and/or such that the number and feedstock of objects in the basis set isvariable. Such an extended problem would lend insight not only intoadvantageous or optimal scan paths, but also advantageous or optimal AMtrack geometry parameters, and the relationships between the two. Anextended problem might also include additional constraints, for example,constraints limiting parameters {P^(j)} according to capabilities of theprinter and the physics of fusing particles or slurry, or constraintsfixing the ratio of different materials in a multi-material problem. Insuch problems, it would be advantageous to have knowledge of trackgeometry for each feedstock at various values of AM track geometryparameters.

Given any solution to the problem, a scan strategy can be extracted fromthat solution based on the geometry of the objects (tracks or trackcross sections) and their positions. To extract the scan strategy, theprinter is required to print, in fabricating a track, with the parameterset {P^(j) _(i)}_(k) that corresponds to the object O_(j,k) in thesolution with that parameter set. The scan path is defined by where theprint head must be positioned and/or deposition of energy and/ormaterial must occur to fabricate an approximation of the object O_(j,k)(or its extrusion, in the case of a track cross section) at its positionin the solution. Most simply for energy deposition, this might bedefined as the center point of the object, though for both energy andmaterial deposition, the specific position, particularly, in thebuild-up direction can vary, as is discussed further below. By way ofexample, a print head that deposits material might need to be positionedon the order of a few track heights above the surface of the articlebeing fabricated in order to fabricate a track, as is shown by way ofexample in FIG. 2.

A solution can be extended over an arbitrary amount of space byreplicating the unit cell to cover the space desired. This concept isdemonstrated for the covering solution presented in FIG. 7 and FIG. 13.With respect to fabricated article outer surfaces, arbitrary contourscans can be defined to border a space covered by an extended solution,meaning that solutions are not article-geometry or slice-geometrydependent insofar as the article or slice lateral extent in a givenlayer is at least as large as one of the objects inside the unit cell.This concept is demonstrated in FIG. 14.

There is flexibility in defining layers from a solution, in that not allobjects in a unit cell might be fabricated in a single layer. Morespecifically, it is not required to define layers, possibly with netdisplacement differing from layers above or below, by assigning a newlayer for all objects with configurations r_(j,k) with object spatialpositions falling at the same displacement in the build-up direction. Anexample of layer definition for the covering solution presented in FIGS.7 and 13 that permits a scan strategy of constant slice thickness (andAM track geometry parameters exhibiting constant net displacement), ispresented in FIG. 15. In this example, the unit cell has been redefinedin order to simplify the implementation of a scan strategy; regardless,the covering solution has not been changed.

Additionally, scan tracks within successive layers need not follow thedirectional orientation suggested by track cross sectional objects in acovering problem solution. For example, in FIG. 16, a depiction of apath-tangent cross section of a covering problem solution derived scanstrategy with a unit cell including two different objects generated fromdifferent AM track geometry parameters employing a powder bed fusion orlaser sintering process, three layers of tracks are shown where thesetracks are all parallel at the cross sectioning plane. In this casehowever, due to small variations in height at the surface of the scantracks printed in each layer or other reasons, rotation every layer,every two layers, or every n layers, might be advisable. FIG. 17 depictstop-down illustration of two successive layers in which a rotation hasoccurred in layer n+1 relative to layer n. For the covering problemsolution demonstrated in FIG. 16, it is additionally not necessary toprint adjacent scan tracks in chronological order; for many processes,it is advantageous to print the smaller tracks in a layer first,followed by the larger tracks. It is further not necessary for thetracks to be straight, as depicted in FIG. 17; arbitrary contours orpaths can be employed. By way of example, FIGS. 18a-c illustrate astrategy where three layers of scans are printed with circular symmetryabout a central point, and FIG. 18d , a path-tangent cross sectionalimage of the three layers along the dot-dash line shown in FIG. 18c ,shows that indeed the same covering problem solution is employed toderive the FIGS. 18a-c strategy as that shown in FIG. 29.

It is sometimes necessary to select an angular orientation for the unitcell in order to define layers; however, the angular orientation of theobjects may be fixed according to the relative location of a print headand/or the directionality of energy and/or material deposition, thusfixing the angular orientation of the unit cell. The angular orientationof the cell might also be fixed in the case of a covering problem solvedaccording to a non-Euclidean geometry, or in other cases as well.Regardless, even in cases where constraints on orientation are imposedduring the solving of the problem, there may be an option to choose inwhich layer certain objects will be printed, and this choice mightdiffer for the same basis object appearing in different cells.Importantly, objects O_(j,k) of different geometry might appear withinthe same layers, or certain layers might be made up only of objects ofone geometry type. In the example presented in FIG. 13, the angularorientation of the objects is fixed according to the position of thelaser, the unit cell most simply includes objects from three differentlayers due the vertical stacking of three different basis objects in thecenter of the cell (though five layers are defined in FIG. 15 in orderto more simply define a scan strategy), and alternating layers containobjects of only one, or objects of two different types, of track crosssection, where the smaller objects are those exhibiting two types oftrack cross section, which are mirror images, due in this example to thediffering surface geometry on which they are printed.

Scan strategies containing objects printed with more than one set of AMtrack geometry parameters can also contain rotations in track directionbetween layers, or every two, three . . . or n layers. By way ofexample, FIG. 19 depicts a rough illustration of scan tracks in a scanstrategy with a rotation of about 90 degrees every two layers derivedfrom the covering problem solution depicted in FIG. 7b . The rotationangle can be chosen to suit desired printed article properties, or toimprove throughput at a given porosity, or for other reasons. Further,tracks need not be straight as shown in FIG. 19, but could consist ofparallel paths of any direction within the surface of the layer,including by way of example the circular pattern shown in FIG. 18.

A global solution to a covering problem is not necessary to produceadvantageous scan strategies; coverings that are locally optimal, orthat have been derived from locally optimal solutions, might even bemore advantageous depending on fabricated article targeted mechanicalproperties or other requirements. For example, covering problemsolutions that are locally optimal often include regions or points ofspace near the borders of objects that are covered by only one object.Due to the fact that scan and track based printing methods tend toproduce tracks that vary stochastically in their local geometry, regionsor points of space near or on the borders of objects that are onlycovered once may be more likely to become regions or points where a lackof fusing of powder or slurry can occur during printing. Consequently,if fewer such lack-of-fusion regions, or similarly, a lower porosityfabricated article is desired, increasing the overlap in these regionsmay be desirable.

This can easily be accomplished by a simple scaling of the unit cell, orby a combination of a scaling and minor readjustment of objectlocations, or by altering the track geometry parameters {P^(j) _(i)}k ofcertain objects in a fashion known to increase object area or volume, orby a combination of all of these methods or other methods as well. FIG.20 demonstrates such an approach for the example shown in FIG. 7. InFIG. 20a , the unit cell is scaled down in the hatch spacing direction,accomplished by reducing the hatch spacing while holding AM trackgeometry parameters fixed. In FIG. 20b , print speed (an AM trackgeometry parameter) is reduced for the smaller objects, resulting indeeper and wider such objects, and these smaller objects areadditionally relocated somewhat lower in the cell to more accuratelyreflect track fabrication given AM track geometry parameters and objectrelative positions.

Cells can be scaled as well as objects, in particular if the geometry ofthe space on which the lattice is defined is curved or scaled. FIG. 21is an example cross section image of tracks printed according to acovering problem solution derived using unit cells on curved and scaledspace with spherical geometry, employing a material jetting, fuseddeposition modeling, arc plasma sintering, multi-jet fusion, binderjetting or similar process. In the case presented in the figure, eachunit cell is curved according to a radial distance r from a centerpoint, and unit cells farther from the sphere center are larger in area(or volume) from those closer to the center point. This implies asimilar spherical geometry to slices and layers. Tracks in this case canbe scaled in size (or potentially shape) according to radial distance asare cells (this would require changes in AM track geometry parameters),or they could be held constant in size and shape. Additionally, tracksmight travel according to curved or straight contours, by way ofexample, around an axis through the center point to its highest point,or in a straight line into the page, but following the arc of thesphere's surface in the build-up direction.

A scan strategy that incorporates tracks of different targeted averagegeometry, such as is created by altering printer, AM track geometry,feedstock, and other parameters, produces fabricated articles that areof a fundamentally different composition than those produced using asingle targeted average geometry. From a materials perspective, scantracks are varied objects that tend to exhibit differentcrystallographic (or disordered, linked) structures and chemicalcomposition based on proximity to the surface of the track, due todiffering cooling rates, molecular diffusion rates, bonding propertiesof polymers, gas absorption rates, etc.. Further, because their surfacesare exposed to the atmosphere (or near-vacuum) of a printer, surfaces ofa track tend to form more oxides, nitrides, carbon compounds, andimpurities as compared to the centers of tracks, even in relativelyinert atmospheres, for example such as 99.99% N2, Ar, or other inertgases, and in near-vacuum. As a result of both of these and otherdifferences, tracks of differing track cross sections cause differencesin fabricated article mechanical, thermal, electrical, and otherphysical properties.

The differences in micro- and macro-structure generated by differentscan strategies and track geometries are demonstrated visually for avariety of materials printed via several processes in FIGS. 12 and22-27. FIG. 22 is a path tangent cross-sectional image, etched usingacid to reveal grain and track boundary structures, of a single layer ofsteel printed in a laser powder bed fusion process employing a laserpower of 250 W, hatch spacing of 140 um, a laser scan speed of 1046mm/s, and a roughly gaussian beam intensity profile shaped by an F-Thetalens with beam waist of about 55 um. This can be compared to FIGS.23-25, which are printed using the same powder and process but differentscan strategies; FIG. 23 is an image of two layers of the “interleaved”strategy discussed in U.S. Pat. Nos. 6,596,224 and 6,677,554; FIG. 24 isan image of a single layer of a strategy based on the covering problemsolution described in FIG. 16; and FIG. 25 is an image of two layers ofa strategy that alternates layers of larger and smaller tracks where thetracks in each successive layer are printed roughly in between those ofthe previous layer.

Track orientation and track size have a significant effect onmacroscopic fabricated article properties. For example, comparing anarticle fabricated from tracks with scan paths always in the X ornegative X direction to an article fabricated from tracks with scanpaths rotating between X, Y, negative X, and negative Y directions, thefirst article will exhibit strongly differing mechanical propertiesincluding but not limited to ductility and tensile strength in the X ascompared to Y direction, where the second article will not. This maysimilarly be the case for thermal and electrical properties.

Scan strategies incorporating tracks of different targeted averagegeometry may be designed with the goal of affecting fabricated articlemechanical, electrical, thermal, and other physical properties. Moregenerally, employing such a designed scan strategy will result in afabricated article of a fundamentally different composition, from themetallurgical and microstructural perspectives, and will impact articlephysical properties. Such a change in composition can be advantageous.By way of example, in FIGS. 7, 16, and 29, the use of tracks with trackcross sections that are of varying height from layer to layer results ina fabricated article with increased shear strength in the Y directionrelative to an article fabricated with tracks of the same geometry. Thisis because in the latter case, the distinct contrast between layers inthe Z direction results in shear planes between each layer, whereas thereduced contrast in the former case does not.

By way of example, FIG. 26 is a cross sectional image, with crosssection taken tangent to half of the tracks and perpendicular to theother half, of a part printed from steel powder with track settingssimilar to those that fabricated the tracks shown in FIG. 25. In thiscase, two layers are printed with parallel (or anti-parallel) tracks,the first with larger tracks generated by slower scan speeds and thesecond with smaller tracks generated by faster scan speeds; then, twomore layers are printed in a similar fashion, but with tracks rotated 90degrees to the first two layers. This process is repeated. Example 3adescribes the differences in porosity achieved by printing at the samelaser power, hatch spacing, beam waist and total deposited energy perunit mass but employing 3 different scan track strategies, demonstratinga substantial reduction in porosity by use of the multi-track geometrystrategy the microstructure of which is shown in FIG. 26. FIG. 32consists of images of parts printed using the three different strategiesand visually demonstrates the differences in porosity. Example 3bdescribes the difference in mechanical properties between couponsprinted according to the single-track strategy described in U.S. Pat.Nos. 6,596,224 and 6,677,554, and those printed according to themulti-track strategy shown in FIGS. 25 and 26. Despite similar porositybetween the coupons printed with the different strategies, there is anincrease in yield strength, ultimate tensile strength, and a substantialincrease in elongation to failure using the track-geometry varyingstrategy. FIGS. 25 and 26 clearly demonstrate the composition of matterfabricated by the strategy with track varying geometry via images of thedifferences in material macro- and micro-structure as compared to thepart fabricated by the strategy with single-track geometry, and Example3b clearly demonstrates the mechanical property differences between thetrack varying and single track strategy.

Example 4 describes the reduction in porosity found when printing in apowder bed fusion machine using a multi-track strategy derived from thecovering problem solution shown in FIG. 16, as compared to printingusing a single track strategy. FIG. 27a , an image of the compositionfabricated in an aluminum alloy using a strategy similar to thetwo-track geometry strategy employed in Fig F, viewed in comparison toFIG. 27b , an image of a part fabricated using the same laser power,hatch spacing, and total deposited energy per unit mass as in thecomposition shown in FIG. 27a but different beam waist and scan tracks,further visually demonstrates the differences in macro- andmicro-structure in single vs. multi-track strategies. Example 6describes advantages to mechanical properties and to porosity in analuminum alloy employing the multi-track strategy shown in FIG. 27arelative to the single track strategy shown in FIG. 27b . FIG. 28demonstrates visually for printing in a nickel superalloy thedifferences in porosity, macro-, and micro-structure between two singletrack and one multi-track strategy, again employing the same laserpower, hatch spacing, beam waist, and total deposited energy per unitmass, but different scan tracks. Example 5 describes the differences inporosity that are achieved, as seen in FIG. 28.

Considering multiple printing processes, material families, single andmulti-track scan strategies, the multi-track composition is fabricatedand demonstrates various advantages relative to parts made using singletrack strategies. Altering print parameters to fabricate multi-trackcompositions with improved physical properties and improvedmanufacturing properties, such as increased machine throughput due tohigher speed of fabrication at comparable porosities, is thus a clearlydesirable approach in various layer and track-based manufacturingprocesses.

Employing a material thickness different from net displacement. As hasbeen previously discussed, material thickness and net displacement aregenerally thought of as the same concept, and along with the slicethickness are termed the layer thickness. However, printers of varioustypes tend to have hardware that is capable, when properly controlled,of individually controlling material (powder) thickness and netdisplacement. Examples of when using a different material thicknessrelative to net displacement can be advantageous to fabricated articleproperties are numerous across various printing methods. Some suchexamples of advantageous usages follow forthwith; however, those thatfollow do not constitute a comprehensive list.

In a binder jetting or similar process, consider a powder that is notfully consolidated when deposited in a layer. If the deposited powderthickness is made to be greater than the net displacement by a factorthat accounts for consolidation upon deposition of a solution thatincludes a binder, then a green part with greater fraction of powderrelative to solution will result. Such consolidation after depositioncan occur, for example, when as the solution is deposited onto powderparticles to form a track, solution surface tension tends to draw powderparticles toward the track center. Consolidation of particles can alsooccur due to surface tension drawing particles toward the track centerduring partial evaporation of the solution in a track, or due to heat orother energy treatment of tracks, or for other reasons. If the amount ofsolution deposited in a track is fixed, and the powder thickness isincreased relative to net displacement, then the result will be, for apowder layer including particles that will consolidate further oncesuspended, a higher concentration of powder particles relative tosolution.

In a powder bed fusion or similar process, the geometry of the track(and track cross section) is dependent on the powder thickness. This canalso be the case for a material jetting process where the materialtracks harden, solidify, or are exposed to an energy source or othermaterial agent in order to cure, harden or solidify. Consequently,altering the powder thickness allows the capability to alter trackgeometry without specifically altering the speed of print. Further, anyporosity that was caused by a dearth of particles in a specific regionof the layer, where the dearth might be due to denudation caused by aneighboring track, uneven layering, or other reasons, could bealleviated by the simple additional presence of powder for a powderlayer thicker than net displacement. That is to say, employing a thickerpowder layer than net displacement can reduce pores caused byuncontrolled (or stochastic) variables in track formation.

FIG. 29 is an illustration of a scan strategy designed from a coveringproblem solution employing multiple track object geometries and sizes,multiple net displacements, alternating order of track printing, andmultiple material thicknesses that are either greater than or equal tothe net displacement within a single layer, depending on the layer. Thisstrategy could be applied, with some modification, in any printingprocess, but track cross section geometry is in this case drawn toreflect tracks generated employing AM track geometry parameters for apowder bed fusion, laser sintering, or possibly a binder jettingprocess.

A thinner powder layer relative to net displacement in a powder bedfusion or similar process might also be advantageous. Though thespecifics of the geometry of a track (and track cross section) aredependent on the AM track geometry and feedstock parameters, parametersare often used such that employing a thinner powder layer will result ina track with more depth and less width as compared to a powder layer ofthickness equal to that of the net displacement. Increasing track depthwhile decreasing track width is advantageous to decreasing porosity inthe cases where hatch spacing is sufficiently small but where there isinsufficient inter-layer fusing and re-fusing to ensure successivelayers are completely fused.

FIG. 30 is a comparison of cross sectional images of parts printed insteel using the same single track scan strategy; however, for the partshown in FIG. 30a , material thickness and net displacement are both 50um, and for the part shown in FIG. 30b , net displacement is 50 um butpowder thickness is 60 um. Improvements in part porosity, macro- andmicro-structure are clearly visible: Example 7 describes the benefit toporosity quantitatively. FIG. 31 is a comparison of cross sectionalimages of parts printed in aluminum using the same multi-track scanstrategy; however, for the part shown in FIG. 31a , material thicknessand net displacement are both 50 um, and for the part shown in FIG. 31b, net displacement is 50 um but powder thickness is 60 um. Improvementsin part porosity, macro- and micro-structure are visible: Example 8describes the benefit to porosity quantitatively.

EXAMPLES

In all examples below, the standard deviations provided are thosecalculated for multiple parts or coupons built at different locations onthe build platform during a single build, unless otherwise specified.

Example 1

In this example, material jetting via a fused deposition modelingprinter with a single 400 um nozzle and a thermoplastic polymer feedwire consisting principally of polylactic acid is deployed to printthree 20 mm cubes, each with different print parameters. Two cubesemploy single track scan strategies with identical printer settingsexcept that each cube is printed with a different extrusion volume ratiosetting, and one cube employs a multi-track scan strategy with the sameparameter settings as for the single track strategy except wherealternation between two extrusion volume ratio settings is employed forprinting successive tracks resulting in two distinct scan trackgeometries, along the lines of the strategy described for FIG. 26. Inthis case, only one cube of each type was printed; therefore, thestandard deviations given for porosities are those measured acrossmultiple images taken at different locations within the cube. Thestandard deviations given for mass are a measure of precision balancerepeatability.

Single Track Cubes:

FIGS. 8 and 9 are cross sectional images of the single track geometrycubes, printed employing the following printer settings (and others nothere listed) on the Prusa i3 machine:

Bed temperature: 40 C

Extruder Temperature: 190 C

Fan Power: 100%

Feed Rate (i.e. speed head moves): 1800mm/s

Hatch Spacing: 400 um

Nozzle Diameter: 400 um

Layer thickness 200 um

Cube 1 extrusion volume ratio: 0.35

Cube 2 extrusion volume ratio: 0.52

Measured porosity for Cube 1 is 8%+/−0.6%, with a total mass of 8.704g+/−0.005g; measured porosity for Cube 2 is 7%+/−1.3% away from theedges, with a total mass of 3.071 g+/−0.005 g, principally because theprint did not complete due to build failure resulting in only about 36%of the “cube” being printed.

Multi-Track Cube:

FIG. 11 is a cross sectional image of the multi-track geometry cube,printed employing the following printer settings (and others not herelisted) on the Prusa i3 machine:

Bed temperature: 40 C

Extruder Temperature: 190 C

Fan Power: 100%

Feed Rate (i.e. speed head moves): 1800 mm/s

Hatch Spacing: 400 um

Nozzle Diameter: 400 um

Layer thickness 200 um

Smaller track extrusion volume ratio: 0.31

Larger track extrusion volume ratio: 0.63

Measured porosity for the multi-track cube is 2.3%+/−0.2%, with a totalmass of 9.260 g+/−0.005 g. It is clear from the data that the amount ofmaterial extruded for a track is not linearly proportional to theextrusion volume ratio setting; however the results of implementing themulti-track strategy are clear: substantially reduced porosity withoutsacrifice of geometric part accuracy or increase in surface roughness.

Example 2

Material jetting via a fused deposition modeling printer with a single400 um nozzle and a thermoplastic polymer feed wire consistingprincipally of polylactic acid is deployed to print three 20 mm cubes,each with different print parameters. Two cubes employ single track scanstrategies with identical printer settings except that each cube isprinted with a different extrusion volume ratio setting, and one cubeemploys a multi-track scan strategy with the same parameter settings asfor the single track strategy except where alternation between twoextrusion volume ratio settings is employed for printing successivetracks resulting in two distinct scan track geometries, along the linesof the strategy described for FIG. 16 and an exemplar image of which isdepicted in Fig D. In this case, only one cube of each type was printed;therefore, the standard deviations given for porosities are thosemeasured across multiple images taken at different locations within thecube. The standard deviations given for mass are a measure of precisionbalance repeatability.

Single Track Cubes:

FIGS. 8 and 9 are cross sectional images of the single track geometrycubes, printed employing the following printer settings (and others nothere listed) on the Prusa i3 machine:

Bed temperature: 40 C

Extruder Temperature: 190 C

Fan Power: 100%

Feed Rate (i.e. speed head moves): 1800 mm/s

Hatch Spacing: 400 um

Nozzle Diameter: 400 um

Layer thickness 200 um

Cube 1 extrusion volume ratio: 0.35

Cube 2 extrusion volume ratio: 0.52

Measured porosity for Cube 1 is 8%+/−0.6%, with a total mass of8.704g+/−0.005g; measured porosity for Cube 2 is 7%+/−1.3% away from theedges, with a total mass of 3.071 g+/−0.005 g, principally because theprint did not complete due to build failure resulting in only about 36%of the “cube” being printed.

Multi-Track Cube:

FIG. 10 is a cross sectional image of the multi-track geometry cube,printed employing the following printer settings (and others not herelisted) on the Prusa i3 machine:

Bed temperature: 40 C

Extruder Temperature: 190 C

Fan Power: 100%

Feed Rate (i.e. speed head moves): 1800 mm/s

Hatch Spacing: 400 um

Nozzle Diameter: 400 um

Layer thickness 200 um

Smaller track extrusion volume ratio: 0.34

Larger track extrusion volume ratio: 0.69

Measured porosity for the multi track cube is 0.2%+/−0.06%, with a totalmass of 9.440 g+/−0.005 g. It is clear from the data that the amount ofmaterial extruded for a track is not linearly proportional to theextrusion volume ratio setting; however the results of implementing themulti-track strategy are clear: the near elimination of porosity withoutsacrifice of geometric part accuracy or increase in surface roughness.

Example 3

In this example, porosity and mechanical property results are describedfor powder bed fusion printing of parts from two 316L stainless steelpowders exhibiting for Example 3a a d50 of 18 um and for Example 3b ad50 of 45 um. Four 1 cm porosity cubes are printed for each of the threestrategies (two single track, one multi-track) with some print settingsdescribed in Example 3a, and three 7.5 cm long (with 2.5 cm gauge)dogbone tensile coupons are printed for each of the two strategies (onesingle track, one multi-track) with some print settings described inExample 3b. The single track approaches in Example 3a deploy the scanstrategies described for FIGS. 32c and 32b , and the multi-trackstrategy deploys the scan strategy described for FIG. 32a . The scanpaths for the single and multi-track strategies in Example 3b aresimilar to those described for FIGS. 32c and 32a , respectively.

Example 3a Porosity

Single Track Cubes

Laser Power: 252 W

Hatch Spacing: 140 um

Gaussian Beam Waist: 55 um

Net Displacement: 50 um

Powder Thickness: 50 um

Scanning Speed: 1190 mm/s

Average measured porosity for the cubes printed according to thestrategy described for FIG. 32b is 0.560%+/−0.073%, and for the cubesprinted according to the strategy described for FIG. 32c , it is1.127%+/−0.147%.

Multi-Track Cubes:

Laser Power: 252 W

Gaussian Beam Waist: 55 um

Hatch Spacing: 140 um

Net Displacement: 50 um

Powder Thickness: 50 um

Scanning Speed Ratio: 1.6

Averaged measured porosity for the cubes printed according to thestrategy described for FIG. 32a is 0.231%+/−0.030%, far lower thanporosity for the single track strategies. In this case, the energydeposited per unit mass (and total print time) for the cubes printed byall three strategies were identical, leading to the clear conclusionthat the multi-track strategy delivers substantially lower porosity forequal energy input and time of print. Taking another angle, the energyinput, and consequently the print time, using the multi-track strategydescribed could have been reduced until the porosity of the cubesproduced was equal to that of one of the single track strategies. Inthis case, the same porosity would have been delivered with aconsiderably faster print speed, thereby resulting in comparable partsacross the strategies but a substantial increase in throughput for themulti-track strategy.

Example 3b

Mechanical Properties

Single Track Tensile Bars:

Laser Power: 252 W

Hatch Spacing: 140 um

Gaussian Beam Waist: 55 um

Net Displacement: 50 um

Powder Thickness: 50 um

Scanning Speed: 1066 mm/s

Multi-Track Tensile Bars:

Laser Power: 252 W

Hatch Spacing: 140 um

Gaussian Beam Waist: 55 um

Net Displacement: 50 um

Powder Thickness: 50 um

Scanning Speed Ratio: 1.6

The energy deposited per unit mass (and total print time) was identicalfor both the single track and multi-track bars printed. All bars wereoriented identically in the build chamber, and scan path directions wereidentical before rotation. However, the total energy deposited per unitmass was greater for the bars printed in Example 3b as compared to thecubes printed for Example 3a. This was to help eliminate thedifferential in porosity between the single and multi-track scanstrategies, such that the tensile properties of the bars could becompared on the basis of roughly equivalently porosity. Additionally tothis end, the change in powder made to print the bars for Example 3b vs.printing the cubes for Example 3a led to further reduced porosity. Thesingle track strategy bars, printed corresponding to the “interleaved”strategy described in U.S. Pat. Nos. 6,596,224 and 6,677,554, exhibitedaverage ultimate tensile strength of 777 MPa+/−10.5 MPa, yield strengthof 621 MPa+/−12.9 MPa, and elongation to failure of 22%+/−1.7%. Themulti-track strategy bars exhibited ultimate tensile strength of 802MPa+/−4.0 MPa, yield strength of 645 MPa+/−16.5 MPa, and elongation tofailure of 36%+/−1.7%.

It is clear from the mechanical property results measured that themulti-track strategy, even at comparable porosity, yields a compositionof matter with multiple mechanical properties that exceed those of theparts printed by the single track strategy. Performing Welch's t-Test tocalculate confidence values, we find that with 96.94% confidence theultimate tensile strength is greater for the multi-track strategyprinted bars, with 92.93% confidence the yield strength is greater forthe multi-track strategy printed bars, and that with 99.97% confidencethe elongation to failure is greater for the multi-track strategyprinted bars. It is therefore clear that the macro- and micro-structuresgenerated by the multi-track strategy produce a different composition,measured by mechanical properties, than that generated by the singletrack strategy.

Example 4

Porosity results are measured for powder bed fusion printing of partsfrom a 316L stainless steel powder similar to that used for the printingof bars in Example 3b. Four 1cm porosity cubes are printed for each ofthe two strategies (one single track strategy, one multi-track), withsome print settings described below. The scan paths for the single trackstrategy are similar to those described for FIG. 32c , and themulti-track strategy is based on the covering problem solution describedin FIG. 16, similar to that described for material jetting in FIG. 12.

Single Track Cubes:

Laser Power: 252 W

Hatch Spacing: 120 um

Gaussian Beam Waist: 55 um

Net Displacement: 50 um

Powder Thickness: 50 um

Scanning Speed: 1161 mm/s

Multi-Track Cubes:

Laser Power: 252 W

Hatch Spacing: 120 um

Gaussian Beam Waist: 55 um

Net Displacement: 50 um

Powder Thickness: 50 um

Scanning Speed Ratio: 1.5

The energy deposited per unit mass (and total print time) was identicalfor both the single track and multi-track cubes printed. Averagemeasured porosity for the cubes printed according to the single trackstrategy was 0.844%+/−0.110%, and for the cubes printed according to themulti-track strategy, it was 0.580%+/−0.076%. Applying Welch's t-Test,it can be stated with 99.46% confidence that the cubes printed from themulti-track strategy achieve reduced porosity relative to the cubesprinted from the single track strategy; this result is in-line withother results measured for comparative printing with these twostrategies.

Example 5

In this example, porosity results are described for powder bed fusionprinting of parts from a nickel superalloy powder with a d50 of 21 um.Four porosity coupons measuring 1×1×0.5 cm are printed for each of threestrategies (two single track, one multi-track) with some print settingsdescribed below. The single track approaches deploy the scan strategiesdescribed for FIGS. 28b and 28c , and the multi-track strategy deploysthe scan strategy described for FIG. 28a . For all cubes, energydeposited per unit mass and total print time were identical.

Single Track Cubes

Laser Power: 269 W

Hatch Spacing: 140 um

Gaussian Beam Waist: 55 um

Net Displacement: 50 um

Powder Thickness: 50 um

Scanning Speed: 1071 mm/s

Average measured porosity for the cubes printed according to thestrategy described for FIG. 28b , the “interleaved” strategy, is0.497%+/−0.065%, and for the cubes printed according to the strategydescribed for FIG. 28c , it is 0.691%+/−0.092%.

Multi-Track Cubes:

Laser Power: 252 W

Gaussian Beam Waist: 55 um

Hatch Spacing: 140 um

Net Displacement: 50 um

Powder Thickness: 50 um

Scanning Speed Ratio: 1.6

Averaged measured porosity for the cubes printed according to thestrategy described for FIG. 28a is 0.117%+/−0.015%, far lower than forthe single track strategies. Given that the total print time and energydeployed were identical, the conclusion is clear that the multi-trackstrategy delivers improvement in structure and efficiency. Takinganother angle, the energy input, and consequently the print time, usingthe multi-track strategy described could have been reduced until theporosity of the cubes produced was equal to that of one of the singletrack strategies. In this case, the same porosity would have beendelivered with a considerably faster print speed, thereby resulting incomparable parts across the strategies but with a substantial increasein throughput for the multi-track strategy.

Example 6

Porosity and mechanical property results are described for powder bedfusion printing of parts from two aluminum alloy (AlSi10Mg) powdersexhibiting for Example 6a a d50 of 32 um and for Example 3b a d50 of 41um. Four 1 cm porosity cubes are printed for each strategy, one singletrack strategy and one multi-track, with some print settings describedin Example 6a, and three 7.5 cm long (with 2.5 cm gauge) dogbone tensilecoupons are printed for two similar strategies (one single track and onemulti-track) with some print settings described in Example 6b. Thesingle track approaches in Examples 6a and 6b deploy the scan pathsdescribed for FIG. 27b , where FIG. 27b is a cross sectional image ofone of the cubes printed for Example 6a, and the multi-track approachesin Examples 6a and 6b deploy the scan paths described for FIG. 27a ,where FIG. 27a is the cross sectional image of one of the cubes printedfor Example 6a.

Example 6a Porosity

Single Track Cubes

Laser Power: 375 W

Hatch Spacing: 220 um

Gaussian Beam Waist: 46 um

Net Displacement: 50 um

Powder Thickness: 50 um

Scanning Speed: 1311 mm/s

Multi-Track Cubes:

Laser Power: 375 W

Gaussian Beam Waist Ratio: 1.3

Hatch Spacing: 220 um

Net Displacement: 50 um

Powder Thickness: 50 um

Scanning Speed Ratio: 1.4

Averaged measured porosity for the cubes printed according to the singletrack strategy described for FIG. 27b is 1.211%+/−0.158%, and averagedmeasured porosity for the cubes printed according to the multi-trackstrategy described for FIG. 27a is 0.663%+/−0.086%, far lower than theporosity for the single track strategy. The energy deposited per unitmass (and total print time) for the cubes printed by both strategieswere identical, leading to the clear conclusion that the multi-trackstrategy delivers substantially lower porosity for equal energy inputand time of print. Taking another angle, the energy input, andconsequently the print time, using the multi-track strategy describedcould have been reduced until the porosity of the cubes produced wasequal to that of the single track strategy. In this case, the sameporosity would have been delivered with a considerably faster printspeed, thereby resulting in comparable parts across the strategies but asubstantial increase in throughput for the multi-track strategy.

Example 6b Mechanical Properties

Single Track Tensile Bars:

Laser Power: 375 W

Hatch Spacing: 180 um

Gaussian Beam Waist: 88 um

Net Displacement: 50 um

Powder Thickness: 50 um

Scanning Speed: 1389 mm/s

Multi-Track Tensile Bars:

Laser Power: 375 W

Hatch Spacing: 180 um

Gaussian Beam Waist Ratio: 1.3

Net Displacement: 50 um

Powder Thickness: 50 um

Scanning Speed Ratio: 1.4

In this case, the energy deposited per unit mass and total print timewere each 3.3% lower for the multi-track print strategy relative to thesingle track strategy. All bars were oriented identically in the buildchamber, and scan path directions were identical. The single trackstrategy bars exhibited average ultimate tensile strength of 386.6MPa+/−7.2 MPa, yield strength of 238.8 MPa+/−2.9 MPa, and elongation tofailure of 3.63%+/−0.05%. The multi-track strategy bars exhibitedultimate tensile strength of 373.9 MPa+/−15.3 MPa, yield strength of234.4 MPa+/−11.5 MPa, and elongation to failure of 8.33%+/−3.37%.

The elongation to failure results measured that the multi-trackstrategy, even given a reduced energy deposited and total print time,yield a composition of matter with elongation to failure that exceedsthe performance of that of the parts printed by the single trackstrategy. Using Welch's t-Test to calculate confidence values, we findthat the ultimate tensile strength and yield strength of the barsprinted with different strategies fall within one standard deviation ofone another, suggesting that they are not distinct; however, we findthat with 93.1% confidence the elongation to failure is greater for themulti-track strategy printed bars. It is apparent therefore the macro-and micro-structures generated by the multi-track strategy produce adifferent and preferable composition, measured by mechanical properties,than that generated by the single track strategy. This resultdistinguishing mechanical properties between the composition and partsgenerated by single track strategies (holding energy deposited per unitmass and print time roughly comparable) with favorable resultsattributed to the multi-track strategy parts is common among othercomparative tests as well. This is due to the fact that the optimizationphase space available to strategies with multiple track geometries isfar greater than that available to strategies incorporating only onetrack geometry.

Example 7

Porosity results are measured for powder bed fusion printing of partsfrom a 316L stainless steel powder similar to that used for the printingof cubes in Example 3b. Four 1 cm porosity cubes are printed for each ofthe two strategies (one single track strategy with equal netdisplacement and powder thickness, one single track strategy withdiffering net displacement and powder thickness), with some printsettings described below. The scan strategies are those described forFIG. 30, where the energy deposited per unit mass (and total print time)was identical for both strategies.

Equal Net Displacement and Powder Thickness:

Laser Power: 252 W

Hatch Spacing: 140 um

Gaussian Beam Waist: 91 um

Net Displacement: 50 um

Powder Thickness: 50 um

Scanning Speed: 1004 mm/s

Unequal Net Displacement and Powder Thickness:

Laser Power: 252 W

Hatch Spacing: 140 um

Gaussian Beam Waist: 91 um

Net Displacement: 50 um

Powder Thickness: 60 um

Scanning Speed: 1004 mm/s

Average measured porosity for the cubes printed according to the equalnet displacement and powder thickness strategy was 0.478%+/−0.062%, andfor the cubes printed according to the unequal net displacement andpowder thickness strategy, it was 0.206%+/−0.027%. Applying Welch'st-Test, it can be stated with 99.94% confidence that the cubes printedfrom the unequal net displacement and powder thickness strategy reducedporosity relative to the cubes printed with equal net displacement andpowder thickness.

Example 8

Porosity results are measured for powder bed fusion printing of partsfrom an aluminum alloy powder with a d50 of 27 um. Four 1 cm porositycubes are printed for each of the two strategies (one multi-trackstrategy with equal net displacement and powder thickness, onemulti-track strategy with differing net displacement and powderthickness), with some print settings described below. The scanstrategies are those described for FIG. 31, where the energy depositedper unit mass (and total print time) was identical for both strategies.

Equal Net Displacement and Powder Thickness:

Laser Power: 650 W

Hatch Spacing: 200 um

Gaussian Beam Waist Ratio: 1.4

Net Displacement: 50 um

Powder Thickness: 50 um

Scanning Speed Ratio: 1.9

Unequal Net Displacement and Powder Thickness:

Laser Power: 650 W

Hatch Spacing: 200 um

Gaussian Beam Waist Ratio: 1.9

Net Displacement: 50 um

Powder Thickness: 60 um

Scanning Speed Ratio: 1.9

Average measured porosity for the cubes printed according to the equalnet displacement and powder thickness strategy was 3.29%+/−0.43%, andfor the cubes printed according to the unequal net displacement andpowder thickness strategy, it was 1.79%+/−0.23%. Applying Welch'st-Test, it can be stated with 99.82% confidence that the cubes printedfrom the unequal net displacement and powder thickness strategy reducedporosity relative to the cubes printed with equal net displacement andpowder thickness. This is the case employing a multi-track scan strategywith an aluminum alloy powder, and it was also the case in the presenceof the single track strategy with steel powder in Example 7.

1. An additively manufactured composition, printed using a scan or trackbased process, or any additive manufacturing process generating layerswith surface geometry similar to that produced by any scan or trackbased process, where within a region of the printed article: a. Tracksor track cross sections exhibit a plurality of geometries (shapes and/orsizes), either within a single layer contained within the region oracross a plurality of successive layers, b. the configurations of thetracks or track cross sections can be characterized by a unit cell,described on the average across tracks or track cross sections inEuclidean or other geometric space, with a basis of no less than two, c.the tracks printed within the unit cell are connected within the cell inthe sense that there is no connected area (volume) of unprinted materialor space within the cell larger than the area (volume) of the largesttrack cross section (track), and d. where portions of or all of at leasttwo adjacent unit cells are present in each layer that is partially orentirely contained within the region.
 2. The composition of claim 1,where within a region of the printed article, the configurations andaverage geometries of tracks or track cross sections form a coveringproblem solution or near-solution including a plurality of unit cellswithin the portion of each layer contained within the region.
 3. Thecomposition of claim 1, wherein track geometry or track cross sectionsare all or nearly all substantially similar to one another within aregion of a layer n, and where in an adjoining region of the successivelayer n+1, track geometry or track cross sections are also all or nearlyall substantially similar to one another, but different from those inlayer n.
 4. The composition of claim 1, wherein a plurality of trackgeometries or track cross sections are employed within a region of orall of at least one layer, and where these track geometries or trackcross sections differ in a coordinated fashion within the regions of thelayer or layers in which they are employed.
 5. The composition of claim1, wherein the tracks are all parallel or anti-parallel.
 6. Thecomposition of claim 1, wherein the tracks in a region of a given layerare rotated by some non-zero angle relative to those in the prior layer.7. The composition of claim 1, wherein the tracks in a region of a givenlayer or layers follow one or more non-straight contours.
 8. Thecomposition of claim 1, wherein the layers on which the tracks in aregion of an article are printed are non-planar.
 9. The composition ofclaim 1, wherein the order of printing of tracks within a region of alayer or layers is such that either adjacent tracks or non-adjacenttracks are printed successively.
 10. The composition of claim 9, whereinthe order of printing is such that all tracks of one geometry areprinted, then tracks of a different geometry are printed.
 11. Thecomposition of claim 2, wherein the geometry (size and/or shape), and/orthe configuration of the tracks printed is non-periodic orquasicrystalline.
 12. A method of additive manufacturing or of designingscan strategies for additive manufacturing, employing a scan or trackbased process, or any additive manufacturing process that generates oris designed to generate layers with surface geometry similar to thatproduced by any scan or track based process, where within a region ofthe article: a. Tracks or track cross sections are targeted to beproduced employing a plurality of AM track geometry parameters, eitherwithin a single layer contained within the region or across a pluralityof successive layers, b. the configurations of the tracks or track crosssections are designed such that, according to their associated additivemanufacturing track geometry parameters, they can be characterized by aunit cell, described on the average across tracks or track crosssections in Euclidean or other geometric space, with a basis of no lessthan two, c. the tracks or track geometries within the unit cell areconnected within the cell in the sense that there is no plannedconnected area (volume) of unprinted material or space within the celllarger than the area (volume) of the largest track cross section(track), and d. where portions of or all of at least two adjacent unitcells are present in each layer that is partially or entirely containedwithin the region.
 13. The method of claim 12, where designed tracks ortrack cross sections exhibit configurations that represent a solution toa two (for track cross section) or three (for tracks) dimensionalcovering problem.
 14. The method of claim 12, wherein tracks or trackcross sections are all or nearly all substantially similar to oneanother within a region of a layer n, and where in an adjoining regionof the successive layer n+1, tracks or track cross sections are also allor nearly all substantially similar to one another, but different fromthose in layer n.
 15. The method of claim 12, wherein a plurality oftracks or track cross sections are employed within a region of or all ofat least one layer, and where these tracks or track cross sectionsdiffer in a coordinated fashion within the regions of the layer orlayers in which they are employed.
 16. The method of claim 12, whereinthe tracks are all parallel or anti-parallel.
 17. The method of claim12, wherein the tracks in a region of a given layer are rotated by somenon-zero angle relative to those in the prior layer.
 18. The method ofclaim 12, wherein the tracks in a region of a given layer or layersfollow one or more non-straight contours.
 19. The method of claim 12,wherein the layers on which the tracks in a region of an article areprinted are non-planar.
 20. The method of claim 12, wherein the order ofprinting of tracks within a region of a layer or layers is designed suchthat either adjacent tracks or non-adjacent tracks are printedsuccessively.
 21. The method of claim 20, wherein the order of printingis designed such that all tracks of one geometry are printed, thentracks of a different geometry are printed.
 22. The method of claim 13,wherein the geometry (size and/or shape), and/or the configuration ofthe tracks designed to be printed is non-periodic or quasicrystalline.23. A method of additive manufacturing or of designing layeringstrategies for additive manufacturing where, within a region of anarticle including all or part of each of one or more layers of thatarticle, the material thickness for a given layer or layers is made todiffer (be greater or lesser than) the slice thickness or netdisplacement of that same layer or layers.
 24. The method of claim 23,where the thickness of material deposited for a region including are orpart of each of a layer or layers of that article is made to differ fromthe net displacement or slice thickness of that same layer or layers insuch a fashion as to alter the average geometric shape and/or size ofscan tracks (and/or track cross sections) within the portions of thelayer or layers encompassed by the region.